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

Evaluate: `int(sec^2x)/(sqrt(tan^2x+16))dx`

Text Solution

Verified by Experts

Since derivative of `tanx ` is `sec^(2)x.`
Let `tanx=t` or `sec^(2)x dx=dt`
`:. int(sec^(2)x)/(sqrt(tan^(2)x+4))dx=int(dt)/(sqrt(t^(2)+2^(2)))`
`=log|t+sqrt(t^(2)+4)|+C`
`=log|tanx+sqrt(tan^(2)x+4)|+C`
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