If `I_(m)=int (sin x+cos x)^(m)dx`, then show that `m l_(m)=(sin x+ cos x)^(m-1)*(sin x- cos x)+2(m-1) I_(m-2)`

I=int(sin2x-cos2x)^(2)dx

I=int(sin^2x)/(1+cos x)dx

int(sin2x)/((1+cos2x)^(2))dx

int(2+sin2x)/(1+cos2 x)dx

Show that '(1-cos 2x + sin x)/(sin 2x + cos x) = tan x'

If I_(m"," n)=int cos^(m)x*cos nx dx , show that (m+n)I_(m","n)=cos^(m)x*sin nx+m I_((m-1","n-1))

If I(m,n)=int_0^1x^(m-1)(1-x)^(n-1)dx , then

If I(m) = int_0^pi ln(1-2m cos x + m^2)dx , then I(1)=

Prove that : int_(0)^(pi) sin^(2m) x. cos^(2m+1) x dx=0

IfI_(m , n)=int_0^(pi/2)sin^m xcos^n xdx , Then show that I_(m , n)=(m-1)/(m+n)I_(m-2,n)(m ,n in N) Hence, prove that I_(m , n)=f(x)={((n-1)(n-3)(m-5)(n-1)(n-3)(n-5))/((m+n)(m+n-2)(m+n-4))pi/4 when both m and n are even ((m-1)(m-3)(m-5)(n-1)(n-3)(n-5))/((m+n)(m+n-2)(m+n-4))}