Evaluate: `int(x^7)/((1-x^2)^5)\ dx` .

Options

A. `(x^(8))/((1-x^(2))^(4))+C`
B. `(1)/(8)(x^(8))/((1-x^(2))^(4))+C`
C. `(1)/(8)(x^(4))/((1-x^(2))^(4))+C`
D. none of these

Answer

B

Explanation

We have , `I=int(x^(7))/((1-x^(2))^(5))dx`
`rArrI=int(sin^(7)theta)/((1-sin^(2)theta)^(5))costheta d theta`, where ` x=sintheta`
`rArrI=inttan^(7)thetasec^(2)thetad theta`
`rArrI=int(tantheta)^(7)d (tantheta)=(1)/(8)tan^(8)theta+C`
`rArr I=(1)/(8)(x^(8))/((1-x^(2))^(4))+C`