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If int 2/(2-x)^2 ((2-x)/(2+x))^(1//3)\ d...

If `int 2/(2-x)^2 ((2-x)/(2+x))^(1//3)\ dx = lambda ((2+x)/(2-x))^mu + c` where `lambda and mu` are rational number in its simplest form then `(lambda+1/mu)` is equal to

A

1

B

2

C

3

D

6

Text Solution

Verified by Experts

The correct Answer is:
c
Let `I=int(e^(x)(2-x^(2)))/((1-x)sqrt(1-x^(2)))dx` then ,
`rArrI=inte^(x)((1+(1-x^(2)))/((1-x)sqrt(-x^(2))))dx`
`=inte^(x){(1)/((1-x)sqrt(1-x^(2)))+sqrt((1+x)/(1-x))}dx`
`rArrI=e^(x)sqrt((1+x)/(1-x))+C`
`thereforelambda=(1)/(2)andmu=1`
Hence , 2 `(lambda+mu)=3`.
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