Advanced Strategy for Integration in Calculus

Our bag of tricks for integration is complete! Now it's time to put all our knowledge to use and evaluating integrals without any context. What strategy should we use in each case? Watch me work through them or pause the clip on each example and give them a try! Remember, we know how to use the substitution rule, integration by parts, and integration by trigonometric substitution. We may have to do other clever manipulations too. You can do it!
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up

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You make it look so easy.

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Robert Zanatta That's one flaw of teacher They may fill you with illusion of knowledge

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@@gretawilliams8799 like do you wanna understand the concepts or not?? lmao how is it illusion if you are actually learning.

[@louisuchihatm2556]

I wish I took my early Trigonometric and Calculus classes seriously. Where has my failure brought me; back to you!

[@Moped12322]

facts especially trig

[@vinzchannel01]

I love your intros He knows a lot about the kinds of stuff, professor dave explains.........OOMMMMMM

[@Talonan]

Blessing in disguise you make the Integrals look easy and very understandable. I am longing for a lecture video like this and I'm glad I found you. I appreciate your effort.

[@gloobark]

11:43 one of the most helpful statements i've heard on the topic

[@dakshbadal7522]

The voices in my head have resumed screaming.

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Thank you very much sir! You are a big help through my education, I check your all kinds of videos.

[@scientifictalks9738]

Thank you prof your vids really helped me get out of fear of integral calculus ❤️

[@iumaiiumai5402]

Best explanations clear cut and simple to understand. I wish I had access to this tutorial when I was doing grade nine. Was looking for this all these years.

[@sandro6691]

Thank you. Your maths videos are very helpful. Way better than the ones at my uni.

[@ericsartin2132]

the way i felt when i solved the check comprehension on my own and got it right was absolutely blissful

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I like your philosophical, strategical approach

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cannot thank you enough!! this is super helpful!!! :)

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[@curtpiazza1688]

Thanx Prof Dave!

[@sercandemir5857]

Great Job!

[@georgekashachila1725]

Well explained

[@hidetsuguhiraki3307]

I can see the degree of your study about integration. Great.

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Amazing video professor.. keep it up.. I solved em all!!

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Nice presentation 💖

[@dakshbadal7522]

If you want him to earn money but can't afford patreon, just watch the whole of the skippable ad

[@Fumbiver]

I don’t think that will help. Ad sense is given only for the unskippable version of a skippable ad.

[@ivoryas1696]

​@@Fumbiver Wait, really? Are you sure?

[@louisuchihatm2556]

When you use integration by parts in the last question of the video, you get another integration by parts: xsin(xPower2)- what is the integral of sin (xpower2)?

[@Bulldoges90]

i also dont understand how he got that integrand. i`m getting a different answer. 2sinx^2 is =-cosx^2/2....but we have xsinx^2

[@programmerpro635]

Just take u = x^2 then du = 2x dx we see there is x on top so we multiply by two on top and take out 1/2 of the integral to make it equal. Then the integral becomes 1/2 sinu du which is -cosu/2 subsitute back for u and you will have your answer.

[@astha_yadav]

i know it's a very late reply, but in case someone sees it- To keep it simpler and less confusing, integrate by keeping it in the substituted form only ie. _usinu du_ , while integrating by parts Then put _u = x^2_ in the final answer

[@astha_yadav]

15:30 This problem can be solved a bit more easily, by keeping the expression in _usinu_ du form while integrating it by parts Then only putting u = x^2 in the end

[@sabihabanu4319]

The next video is not coming !! Btw u r just awesome !!

[@neoking101]

super helpful prof ❤

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This is the only man I'll watch the entire ad for

[@nikianderson2847]

I watched this before my exam took notes and think I might have passed my exam. Thank you!

[@user-yw8pr8wp4b]

Thanks

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excellent

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Wow u made all these master pieces within 1 day ? I just noticed what you wear.

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Wow!

[@auswinbertin3306]

Please do a video about matrices

[@ProfessorDaveExplains]

linear algebra is coming soon!

[@billybutcherr69]

Try something , if it doesn't work try something else - Prof. Daves 12:26

[@11stemgen1dinoeldinjr.d.de8]

I tought I'm the only one confused at 6:53, until I saw it was most replayed, hahahah.

[@sarahm.7514]

Hi, would you be able to make a video on partial fraction decomposition method for integration?

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Are you an A level student? I study those too! This dude is a wonderful teacher.

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Man u da best

[@fireblast3740]

4:13 - No need - (sqrt(u))'=1/(2sqrt(u)) ;F(1/(2sqrt(u))=sqrt(u). No need do more that need

[@rjashtaputre]

Superb explanations. Thanks a lot for sharing. By the way, I didn't get a point here, why can't we evaluate ∫cos√x.dx to -sin√x+c? that looks pretty straight forward, right? And also, I found sometimes the constant hasn't been added after evaluating the indefinite integrations. How does it actually work?

[@Tallyoh]

I’m not sure what your thinking is but the integral of cos(sqrtx) is not that. try taking the derivative of -sin(sqrtx) you will get something different. So no it’s not that straight forward.

[@astha_yadav]

we can't because √x is considered a function itself so, cos√x is cos of a function of x let's say x is an angle, so cos(x) is valid but √x is not an angle, it's a function of the angle x

[@thatsnotme3235]

WOW

[@gabedarrett1301]

How do you prove that it's literally impossible to integrate certain expressions?

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Love from INDIA❤️❤️❤️❤️❤️

[@aidanperreault9951]

The GOAT

[@TheBrammiej]

Didnt know integrals were so awesome!

[@bathtubanarchy]

I don't understand how the 2x on the right hand side of the second to last line of the comprehension disappears.

[@bathtubanarchy]

Finally got there. ∫ [- (cos^2)/2] 2x dx The 2s cancel out, leaving ∫ - (cos x ^2) x dx pull - through, - ∫ (cos x ^2) x dx use substitution, u = x^2 therefore du/dx = 2x. Move dx to the other side. du = 2x dx. Divide by 2 to get x dx on its own, to match what's left in the original expression after substitution du/2 = x dx -∫ cos u * (du/2), break du/2 into du * 1/2 -∫ cos u * du * 1/2, pull 1/2 through - 1/2 ∫ cos u du, ∫ cos u du is a standard trig integration, ∫ cos u du => sin u -1/2 * sin u. Combine terms -(sin u /2) replace u with substitute term. - (sin x^2)/2

[@jackhuang6264]

there is an erro in 2:30 which the anti-derivative of tanx is wrong

[@ProfessorDaveExplains]

no these are all correct

[@jackhuang6264]

@@ProfessorDaveExplains I'm really sorry, I made a silly mistake

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I thick end of this year or next year you will have 1 million subscribers.

[@ProfessorDaveExplains]

I'm gonna get there in about four weeks.

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@@ProfessorDaveExplains you deserve it. you already probably know, but highlighting what is being talked about in red is what separates you from other youtubers. the viewer never gets lost! it's great!

[@tack3545]

this is hard fr

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Dis trippy bruh

[@jjy365959]

That’s me in 9:52

[@fortun8diamond]

You are right, just like chess, it's an art.

[@aMartianSpy]

The you is dizzy.

[@dnz_yt5]

Hello professor dave, I hope you would notice me, this u-subtitution method.. I used this on my test. All my answers were marked wrong, I follow exactly how would you manipulate the problem so it will look alike as the basic formula for integration. However he invalidate my reasons that I learned it on KZbin, I had lots of references. Your Videos, The Organic Chemistry Tutor, and more youtubers and registered Mechanical engineers. What he said was it was too complicated for him to look our papers. Idk what to say to him, he's a registered and topnotcher on board exam, way back 90s. He just invalidate our reasons. We are not taught in school these calculus things, we are just given the coverage and after a few weeks he gives the test. No teaching, we are purely self-paced learning. Please help me, how would I let him know that this kind of method / technique exists. We showed him the demo of how it is solve he just keep invalidating our reasons.

[@angelisvegan5826]

1:53 i can spot a mistake there in your chart.. Integral of a^x is equal to a^ x times lna) ie ¶a^x = a^x.lna + c

[@luminousvalentine8011]

Isn't that the rule for exponential derivative

[@aadityasahoo3352]

thats the derivative :\

[@dailyrosesofholyquran780]

Ur methodology quite differs from others

[@thatsnotme3235]

AOW

[@MH-ue5ct]

Can u solve one proplem for me?

[@xenomorphbiologist-xx1214]

Thank you Chemistry Jesus!

[@marius4363]

I don"t think this can be called advanced

[@ignitestudios7039]

haha hard to tell if you are talking to me or refering to the substitution "u", pretty funny if you think about it

[@Ahrceon]

man wtf

[@HellooDae]

I put a dislike cause I didn't understand this video.

[@Flameville]

Integration is not like a sport...math is nothing like a sport. Math is just frustrating.

[@omarmaya1263]

Just need to practice

[@ian.ambrose]

Being good at it will make frustration go away.