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Evaluate: inttan^(-1)((3x-x^3)/(1-3x^2))...

Evaluate: `inttan^(-1)((3x-x^3)/(1-3x^2))\ dx`

Text Solution

Verified by Experts

`x=tan theta`
` Rightarrow d x=sec ^{2} theta d theta`
We know that,
`frac{3 tan theta-tan theta^{2}}{1-3 tan theta^{2}}=tan 3 theta `
` I=int tan ^{-1}(frac{3 tan theta-tan theta^{3}}{1-3 tan theta^{2}}) sec ^{2} theta d theta`
...
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