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int x.2^(ln(x^(2)+1))dx is equal to...

`int x.2^(ln(x^(2)+1))dx` is equal to

A

`(2^(ln(x^(2)+1)))/(2(x^(2)+1))+C`

B

`(x^(2)+1)2^(ln(x^(2)+1))/(ln2+1)`

C

`((x^(2)+1)^(ln2+1))/(2(ln2+1))+C`

D

`((x^(2)+1)^(ln2))/(2(ln2+1))+C`

Text Solution

Verified by Experts

The correct Answer is:
C
`I=intx2^(ln(x^(2)+1))dx`
Let `x^(2)+1=t,rArr xdx=(dt)/(2)`
Hence `I=(1)/(2)int2^(lnt)dt`
`=(1)/(2)intt^(ln2)dt`
`=(1)/(2).(t^(ln2+1))/(ln2+1)+C`
`=+(1)/(2).((x^(2)+1)^(ln2+1))/(ln2+1)C`
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