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

int x^(3)cos x^(4)dx int nx^(n-1)cos x^(n)dx

int (x ^(n-1))/( x ^(2n) + a ^(2)) dx =

int((cos x)^(n-1))/((sin x)^(n+1))dx=(A)-(cot^(n)x)/(n)+c(B)-(cot^(n)x)/(n+1)+c(C)(cot^(n)x)/(n)+c(D)(cot^(n)x)/(n+1)+c

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

If I_(n)=int x^(n)cos axdx and I_(n)=int x^(n)sin axdx then show that.(1)aI_(n)=x^(n)sin ax-nI_(n-1)

int x ^ (2n-1) cos x ^ (n) dx

int(2x^(n-1))/(x^(n)+3)dx

If quad A_(n)=int_(0)^((pi)/(2))(sin(2n-1)x)/(sin x)dx;B_(n)=int_(0)^((pi)/(2))((sin nx)/(sin x))^(2)dx; for n in N, then

If I_(n)=int_(0)^( pi)e^(x)(sin x)^(n)dx, then (I_(3))/(I_(1)) is equal to