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

$$\int \frac{{\tan }^3\left(\ln x\right)}{x}dx=??$$

Commented by bobhans last updated on 04/Jun/20

$$\mathrm{u}=\ln \left(\mathrm{x}\right)\Rightarrow \int \tan {}^3\mathrm{u}\mathrm{du}=\int (\sec {}^2\mathrm{u}-1)\tan \mathrm{u}\mathrm{du}$$$$=\frac{1}{2}\tan {}^2\mathrm{u}+\ln \mid \cos \mathrm{u}\mid +\mathrm{c}$$$$=\frac{1}{2}\tan {}^2(\ln \mid \mathrm{x}\mid )+\ln \mid \cos \ln \mid \mathrm{x}\mid \mid +\mathrm{c}$$

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

$$\mathrm{perfect}$$

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