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Integrate the following respect to x. ...

Integrate the following respect to x.
(i) `(xsin^(-1)x)/(sqrt(1-x^2))` (ii) `x^5e^(x^2)`
(iii) `tan^(-1)((8x)/(1-16x^2))` (iv) `sin^(-1)((2x)/(1+x^2))`

Text Solution

Verified by Experts

The correct Answer is:
(i) `-sin^(-1)xsqrt(1-x^2)+x+c`
(ii) `e^(x^2)/2[x^4-2x^2+2]+c`
(iii) `=1/2[4xtan^(-1)(4x)-log|sqrt(1+16x^2)|]+c`
(iv) `2[x tan^(-1)x-log|sqrt(1+x^2)|]+c`
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