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Evaluate: (i) int1/(sqrt(x)(sqrt(x)+1))\...

Evaluate: (i) `int1/(sqrt(x)(sqrt(x)+1))\ dx` (ii) `inttan2xtan3xtan5x\ dx`

Text Solution

Verified by Experts

We have given
(i) `int1/(sqrt(x)(sqrt(x)+1))\ dx`
Let `(sqrt(x)+1)=t`
`(1/(2sqrtx))dx=dt`
Then,
`I=(2dt)/t`
`I=2log|t|+c`
`I=2log|sqrt(x)+1|+c`
(ii)`inttan2xtan3xtan5xdx`
...
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