# Help for Integration (2)

$\large \int \sqrt[3]{\tan x} \, dx = \, ?$

Note by Rishabh Deep Singh
2 years, 2 months ago

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I went for 3 substitutions, $$tanx=u^{1/3}$$, $$u=tan\theta$$,
$$\cos2\theta=t$$. Some identities which i used are, $1+x^6=(1+x^2)(x^4-x^2+1)$ $1+\cos2\theta=2\cos^{2}\theta$ $1-\cos2\theta=2\sin^{2}\theta$ $\sin2\theta=2\sin\theta\cos\theta$ $tan^{-1}x + tan^{-1}y=tan^{-1}{\dfrac{x+y}{1-xy}}$ I think this will get you through.

- 2 years, 1 month ago