`int(x-a)(x^(n-1)+x^(n-2)a+...+a^(n-1))dx` where `n` is `+ve` integer =

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

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

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

Solve (x-1)^(n)=x^(n), where n is a positive integer.

int(1)/(x(x^(n)+1))dx

int(dx)/(x^(n)(1+x^(n))^((1)/(n)))

Evaluate int_(0)^(1)(tx+1-x)^(n)dx , where n is a positive integer and t is a parameter independent of x . Hence , show that

Prove that (nC_(0))/(x)-(n_(C_(0)))/(x+1)+(^nC_(1))/(x+2)-...+(-1)^(n)(n_(n))/(x+n)=(n!)/(x(x+1)...(x-n)) where n is any positive integer and x is not a negative integer.

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