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Read the following passages and answer t...

Read the following passages and answer the following questions (7-9)
Consider the integrals of the form `l=inte^(x)(f(x)+f'(x))dx` By product rule considering `e^(x)f(x)` as first integral and `e^(x)f'(x)` as second one, we get `l=e^(x)f(x)-int(f(x)+f'(x))dx=e^(x)f(x)+c`
`l=inte^(x)(tan^(-1)x+(2x)/((1+x^(2))^(2)))dx` then l is equal to

A

`e^(x)(tan^(-1)x-(1)/(1+x^(2)))+c`

B

`e^(x)(tan^(-1)x+(1)/(1+x^(2)))+c`

C

`e^(x)(tan^(-1)x+(2)/(1+x^(2)))+c`

D

`e^(x)(tan^(-1)x-(2)/(1+x^(2)))+c`

Text Solution

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The correct Answer is:
A
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