`int_0^(pi/2)cos2xlogsinx dx`

Evaluate the following integral: int_0^picos2xlogsinx\ dx

Evaluate the following integral: int_0^picos2xlogsinx\ dx

Evaluate int_0^(pi/2) cos^2x dx

The value of the integral sqrt2 int_0^(pi/2) f(sin2x) sinx dx=A (sqrt2/9) int_0^(pi/4) f(cos2x)cosx dx then the value of A is

Prove that: int_0^(pi//2)logsinx\ dx=\ int_0^(pi//2)logcosx\ dx=-pi/2log2

Prove that: int_0^(pi//2)logsinx\ dx=\ int_0^(pi//2)logcosx\ dx=-pi/2log2

Evaluate: int_0^(pi//2)cos^2x\ dx

int_0^(pi//2) x^2 cos 2x dx

Suppose I_1=int_0^(pi/2)cos(pisin^2x)dx and I_2=int_0^(pi/2)cos(2pisin^2x)dx and I_3=int_0^(pi/2) cos(pi sinx)dx , then