Show that `int sin^n x dx=(-sin^(n-1)x.cosx)/n+(n-1)/n` `int sin^(n-2) n dx` also find `int sin^6 dx`

Show that int sin^(n)xdx=(-sin^(n-1)x*cos x)/(n)+(n-1)/(n)int sin^(n-2)ndx also find int sin^(6)dx

int sin^(n)(sin^(-1)x)dx

int x^(n-1)sin x^(n)dx

Show that int x ^(n) . e ^(-x) dx= -x^(n) e ^(-x) +n int x ^(n-1) . e ^(-x) dx

If I_(n)=int sin^(n)x dx , show that, I_(n)=-(1)/(n) sin^(n-1)x cosx+(n-1)/(n).I_(n-2) . Hence, evaluate, int sin^(6)x dx .

Show that int_(0)^(pi//2) sin^(n)xdx =int_(0)^(pi//2) cos^(n)x dx .

int(cos^(n-1)x)/(sin^(n+1)x)dx,n ne 0 is :

The value of the integral int_0^pi (x sin^(2n) x)/(sin^(2n) x + cos^(2n) x)dx is :

int ( n sin^(n-1))/(secx (sin x)^(n)) dx equals :

int ( n sin^(n-1))/(secx (sin x)^(n)) dx equals :