underset(0)overset(oo)int (x)/((1+x)(1+x...

`underset(0)overset(oo)int (x)/((1+x)(1+x^(2)))dx`

Verified by Experts

The correct Answer is:

`pi/4`

underset(0)overset(a)int (1)/(x+sqrt(a^(2)-x^(2)))dx
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underset(0)overset(pi//2)int (sin^(n)theta)/(sin^(n)theta+cos^(n)theta...
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underset(0)overset(oo)int (x)/((1+x)(1+x^(2)))dx
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underset(0)overset(pi//2)int (2log cos x-log sin 2x)dx
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underset(0)overset(pi)int x sin x cos^(4)xdx
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underset(0)overset(pi)int (x tanx)/(sec x "cosec x")
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underset(0)overset(pi)int x sin^(3)xdx
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underset(0)overset(pi)int x cos^(2)xdx
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underset(-1)overset(1)int log((2-x)/(2+x))dx
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underset(0)overset(pi)int log(1+cosx)dx
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underset(0)overset(1)int cot^(-1)(1-x+x^(2))dx
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underset(0)overset(2)int sqrt(2-x)dx
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I=underset(0)overset(2pi)int cos^(5)xdx
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underset(0)overset(1)int (log(1+x))/(1+x^2)dx
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underset(0)overset(oo)int (log x)/(1+x^(2))dx
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underset(0)overset(pi)int x log sin xdx
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underset(0)overset(pi)int (x sin x)/(1+sin x)dx
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underset(0)overset(pi//2)int (x sin x cos x)/(sin^(4)x+cos^(4)x)dx
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underset(0)overset(pi)int (xdx)/(1+sin x)
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underset(0)overset(2pi)int (dx)/(1+e^(sin x))
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