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int(3^(x))/(sqrt(9^(x)-1))dx is equal to...

`int(3^(x))/(sqrt(9^(x)-1))dx` is equal to

A

`(1)/(log3)log|3^(x)+sqrt(9^(x)-1)|+c`

B

`(1)/(log3)log|9^(x)+sqrt(9^(x)-1)|+c`

C

`(1)/(log9)log|3^(x)+sqrt(9^(x)-1)|+c`

D

`(1)/(log9)log|3^(x)-sqrt(9^(x)-1)|+c`

Text Solution

Verified by Experts

The correct Answer is:
A
Let `l=int(3^(x))/(sqrt(9^(x)-1))dx`
Put `3^(x)=t and 3^(x)dx=(1)/(log3)dt`
`thereforel=(1)/(log3)int(dt)/(sqrt(t^(2)-1))`
`=(1)/(log3)[log|3^(x)+sqrt(9^(x)-1)|]+c`
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