Mis-2348 Integrate x ln(1 + x^2)/(1 + x^4)dx from 0 to 1 #calculus #definite_integrals #sneaky #substitution #cipher
Пікірлер: 13
@bokiiibrother9995Күн бұрын
That 2nd substitute is incredibly good ❤
@cipherunityКүн бұрын
Thanks
@Chris_3872 күн бұрын
Nice video, may I suggest you an integral? But I have to send it as an image.
@cipherunity2 күн бұрын
I shall look into it.
@fengshengqin69932 күн бұрын
So here is the question about this substitution : How could you jump to this type ? The process in your mind is the key . Could you help to share it ?
@cipherunityКүн бұрын
The 2nd substitution is very powerful. I used it in many places. It helps you to divide the logarithmic term in the numerator to suitable factors.
@qwertyman1232 күн бұрын
what do you think of the algebra problem also i have a fascinating number theory problem
@cipherunity2 күн бұрын
I can look into it
@qwertyman1232 күн бұрын
@@cipherunity Let n be a positive integer and p a prime, both greater than or equal to 2. Suppose n divides p-1 and p divides n^3 -1. Prove 4p-3 is a perfect square. n divides p-1 -> n p. But this contradicts that n =2, k>=1: we may conclude n-k-1 = 0, or k = n-1. Then 4p-3 = 4(n(n-1)+1) - 3 = 4n^2 - 4n + 4-3 = 4n^2 - 4n + 1 = (2n-1)^2. The proof is complete.
@cipherunity2 күн бұрын
@@qwertyman123 saved
@qwertyman1232 күн бұрын
@@cipherunity is the algebra problem good
@cipherunity2 күн бұрын
@@qwertyman123 I just saved it. But still I need to read it.