x = tan m dx = ^2m dm ∫tan^ 1(3tan m tan^3m1 3tan^2m) ^2m dm ∫tan^ 1 (tan3m) ^2mdm ∫ 3m ^2m dm 3m tan m 3∫tan m dm 3x tan^ ...

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Functions

∫tan-13x-x31-...

Question

$\int {tan}^{- 1} (\frac{3 x - x^{3}}{1 - 3 x^{2}}) d x$ .

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Solution

$x = tan m$
$d x = {sec}^{2} m d m$
$\int {tan}^{- 1} (\frac{3 tan m - {tan}^{3} m}{1 - 3 {tan}^{2} m}) {sec}^{2} m d m$
$\int {tan}^{- 1} (t a n 3 m) {sec}^{2} m d m$
$\int 3 m {sec}^{2} m d m$
$3 m tan m - 3 \int tan m d m$
$3 x {tan}^{- 1} x + 3 ln | cos \frac{1}{\sqrt{1 + x^{2}}} |$

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Similar questions

\int_{0}^{1}

^{- 1} (\frac{3 x - x^{3}}{1 - 3 x^{2}}) d x

\int \tan^{- 1} (\frac{3 x - x^{3}}{1 - 3 x^{2}}) d x

x > \frac{1}{\sqrt{3}}

t a n^{- 1} x

\int_{0}^{1 / \sqrt{3}} \tan^{- 1} (\frac{3 x - x^{3}}{1 - 3 x^{2}}) d x

t a n^{- 1} x + t a n^{- 1} \frac{2 x}{1 - x^{2}}

t a n^{- 1} \frac{3 x - x^{3}}{1 - 3 x^{2}}

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