Integral of tan^4(x) = Integral of y^4/(y^2+1) ?? - Change of Variable

[@frustrateddudehere2846]

Hello sir, can we just now take it as a rule : integral of tan^n(x) = tan^n-1(x)/n-1 - tan(x) + x + c ? I appreciate your videos, hope you are doing well during these hard times

[@MasterWuMathematics]

Good thinking, but not quite. The reduction formula is actually ∫tan^n(x)dx = tan^(n-1)(x) / (n-1) - ∫tan^(n-2)(x)dx. So for integrating powers of tan(x), you would apply it repeatedly until you get a power of tan(x) that you can manage. The term tan(x) + x is result of the integral of tan^2(x) when you apply the reduction formula to ∫tan^4(x)dx. See this video: kzbin.info/www/bejne/o6GXo2mwqZl-mqs. I made this video to show how you can use some mathematical ingenuity to transform a seemingly difficult problem to a series of easier integrals. I appreciate your comment. I'm doing well, I hope you are too. Don't be "Frustrated". Keep asking questions!

[@phuocnhutle6190]

Very good👏

[@MasterWuMathematics]

Thank you! Cheers!

[@a-k-j]

Thanks.

[@MasterWuMathematics]

No worries!