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int(((x^(2)+2)a^((x+tan^(-1)x)))/(x^(2)+...

`int(((x^(2)+2)a^((x+tan^(-1)x)))/(x^(2)+1))dx` is equal to

A

`log a.a^(x+tan^(-1)x)+c`

B

`((x+tan^(-1)x))/(loga)+c`

C

`(a^(x+tan^(-1)x))/(loga)+c`

D

`loga(x+tan^(-1)x)+c`

Text Solution

Verified by Experts

The correct Answer is:
C
Let `l=int((x^(2)+2)a^((x+tan^(-1)x)))/(x^(2)+1)dx`
`"Put "x+tan^(-1)x=t`
`rArr" "(1+(1)/(1+x^(2)))dx=dt`
`rArr" "(2+x^(2))/(1+x^(2))dx=dt`
`therefore" "l=inta^(t)dt=(a^(t))/(loga)+c=(a^(x+tan^(-1)x))/(loga)+c`
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