tan-3-ln-x-x-dx-

Question Number 96699 by Rio Michael last updated on 04/Jun/20

\int \frac{\tan^{3} (\ln x)}{x} d x = ? ?

Commented by bobhans last updated on 04/Jun/20

u = \ln (x) \Rightarrow \int \tan^{3} u du = \int (\sec^{2} u - 1) \tan u du

= \frac{1}{2} \tan^{2} u + \ln ∣ \cos u ∣ + c

= \frac{1}{2} \tan^{2} (\ln ∣ x ∣) + \ln ∣ \cos \ln ∣ x ∣∣ + c

Commented by Rio Michael last updated on 04/Jun/20

perfect