Evaluate the following integral: `int_0^(pi//2)(cos x)/(1+sin^2x)dx`

Explanation

Given,`int_0^(pi//2)(cos x)/(1+sin^2x)dx`

Put sinx=t and cosxdx=dt.

[x=0⇒t=0] and` [x=π/2​⇒t=1]`
.
`I=int_0^1​ dt/(1+t^2)`
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`=[tan^(−1)t]_0^1​ =tan^(−1)(x/a)​+C`


`=π/4​−0`
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`=π/4`​.