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If int(e^(x)(1+100x^(99)-x^(200)))/((1-x...

If `int(e^(x)(1+100x^(99)-x^(200)))/((1-x^(100))sqrt(1-x^(200)))dx=e^(x)((1-x^(k))/(1+x^(l)))^(m)+c`, then

A

`k = 100, n=1`

B

`l=99, m=(1)/(2)`

C

`k=99, m=1`

D

`k=100, m=-(1)/(2)`

Text Solution

Verified by Experts

The correct Answer is:
D
`l=inte^(x)(sqrt((1+x^(100))/(1-x^(100))))=(100x^(99))/((1-x^(100))sqrt(1-x^(200)))`
Now `(d)/(dx)(sqrt((1+x^(100))/(1-x^(100))))=(100x^(99))/((1-x^(100))sqrt(1-x^(200)))`
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