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int(0)^((pi)/(2))log(tanx)dx=0...

`int_(0)^((pi)/(2))log(tanx)dx=0`

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The value of int_(0)^((pi)/(2))log(tan x)dx is equal to -

int_(0)^((pi)/(2))log(sinx)dx=int_(0)^((pi)/(2))log(cosx)dx=(pi)/(2)log.(1)/(2)

Prove that, int_(0)^(pi)log(1+cos x)dx=-pi log2 , given int_(0)^((pi)/(2))log((sin x))dx=(pi)/(2)"log"(1)/(2) .

The value of int_(0)^((pi)/(2))sin2x log(tanx)dx is equal to -

int _(0)^(pi/2) log(cotx)dx

The value of int_0^(pi/2)log(tanx)dx is

Prove that, int_(0)^(pi)f(sinx)dx=2int_(0)^((pi)/(2))f(sinx)dx .

Show : int_(0)^((pi)/(2))sinxf(sin2x)dx=int_(0)^((pi)/(2))cosxf(sin2x)dx

Evaluate: int_(0)^((pi)/(4))log(1+tantheta)d theta

int_(0)^((pi)/(2))(sqrt(sinx)dx)/(sqrt(sinx)+sqrtcosx)