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Evaluate int(0)^(pi//4) log (1+tan theta...

Evaluate `int_(0)^(pi//4) log (1+tan theta)d theta`

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The correct Answer is:
`I=(pi)/(8)(log 2)`
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VMC MODULES ENGLISH-INTEGRAL CALCULUS - 2 -JEE Advanced (Archive)
  1. int(-pi)^(pi) ( e^(sin x ))/( e^(sinx) + e^(-sinx))dx is equal to

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  2. Prove that int(0)^(1)tan^(-1)(1/(1-x+x^(2)))dx=2int(0)^(1)tan^(-1)xdx....

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  3. Evaluate int(0)^(pi//4) log (1+tan theta)d theta

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  4. about to only mathematics

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  5. Evaluate int(-1//sqrt(3))^(1//sqrt(3)) (x^(4))/(1-x^(4)) "cos"^(-1)((2...

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  6. Evaluate: int2^3(2x^5+x^4-2x^3+2x^2+1)/((x^2+1)(x^4-1))dx

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  7. A cubic function f(x) vanishes at x=-2 and has relative minimum/maximu...

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  8. Evaluate: int0^pi(xsin2xsin(pi/2cosx)/(2x-pi)dx

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  9. Prove that for any positive integer k ,(sin2k x)/(sinx)=2[cosx+cos3x+...

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  10. If fa n dg are continuous function on [0,a] satisfying f(x)=f(a-x)a n ...

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  11. The value of the integral overset(2a)underset(0)int (f(x))/(f(x)+f(2a-...

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  12. int0^1log(sqrt(1-x)+sqrt(1+x))dx equals:

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  13. Evaluate int(0)^(pi)(x dx)/(1+cos alpha sin x),where 0lt alpha lt pi.

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  14. Evaluate : int0^(pi/2)(xsinxcosx)/(sin^4x+cos^4x)\ dx

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  15. Evaluate: int0^(1/2)(xsin^(-1)x)/(sqrt(1-x^2))dx

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  16. int(0)^(pi//4)(sin x + cos x)/(9+16 sin 2 x )

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  17. Show that int(0)^(pi)xf(sinx)dx=(pi)/2 int(0)^(pi)"fr"(sinx)dx.

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  18. Find the value of int(-1)^(3/2)|xsinpix|dx

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  19. Evaluate int(0)^(1)(tx+1-x)^(n)dx, where n is a positive integer a...

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  20. The value of int0^1 4x^3{(d^2)/(dx^2)(1-x^2)^5}dx is

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