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Evaluate: int(-pi//4)^(pi//4)(sec^2x)/(e...

Evaluate: `int_(-pi//4)^(pi//4)(sec^2x)/(e^(2x)-1)dx`

Text Solution

Verified by Experts

Let `g(x)=frac{e^{x} sec ^{2} x}{e^{2 x}-1}`
Now,` g(-x)=frac{e^{-x} sec ^{2}(-x)}{e^{-2 x}-1}=-frac{e^{x} sec ^{2} x}{e^{2 x}-1}=-g(x)`
g(x) is and odd function.
Therefore,` I=int_{-pi / 4}^{pi / 4} frac{e^{x} sec ^{2} x d x}{e^{2 x}-1}=0`
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