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Evaluate: (i) int(sec^2x)/(sqrt(16+tan^2...

Evaluate: (i) `int(sec^2x)/(sqrt(16+tan^2x))\ dx` (ii) `int1/(x\ sqrt((logx)^2-5))\ dx`

Text Solution

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(i)`int(sec^2x)/(sqrt(16+tan^2x))\ dx`
let `tanx=t`
`sec^2xdx=dt`
I=`int(1)/(sqrt(4^2+t^2))\ dx`
`I=log(t+sqrt(4^2+t^2))+C`
`I=log(tanx+sqrt(16+tan^2x))+C`
(ii) `int1/(x\ sqrt((logx)^2-5))\ dx`
...
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