`I=int x sinxdx`

Evaluate: inte^(-x)sinxdx

I=int 1/x logx dx =

Evaluate: (i) int sin( x-a)/ sinx dx (ii) int sinx/sin(x-a )dx

int(e^xsinx+cotx+xsinx)/sinxdx

Statement 1: int(sinxdx)/x ,(x >0), cannot be evaluated. Statement 2: Only differentiable functions can be integrated.

If I_1=int_0^(pi/2)f(sinx)sinxdx and I_2=int_0^(pi/2)f(cosx)cosxdx then I_1/I_2

If k is an integer, evaluate int_0^pi (sin2kx)/sinxdx

Show that: int_0^(pi//2)f(sin2x)sinxdx=sqrt(2)int_0^(pi//4)f(cos2x)cosxdxdot

Show that: int_0^(pi//2)f(sin2x)sinxdx=sqrt(2)int_0^(pi//4)f(cos2x)cosxdxdot

Show that: int_0^(pi//2)f(sin2x)sinxdx=sqrt(2)int_0^(pi//4)f(cos2x)cosxdxdot