Prove that `int(dx)/((1+x^2)^(n))=1/(2(n-1))[x/((1+x^2)^(n-1))+(2n-3)int(dx)/((1+x^2)^(n-1))],n in N,` Hence, computer the value of `int cos^4x dx.`

Prove that int(dx)/((1+x^(2))^(n))=(1)/(2(n-1))[(x)/((1+x^(2))^(n-1))+(2n-3)int(dx)/((1+x^(2))^(n-1))],n in N Hence,computer the value of int cos^(4)xdx

int(1)/((x^(2)+k)^(n))dx

Given that int (dx)/((1+ x ^(2))^n)=(x)/(2 (n-1)(1+x^(2) )^(n-1))+((2n -3))/(2(n-1))int (dx)/((1+ x ^(2))^(n-1)). Find the vlaue of int _(0)^(1) (dx)/((1+x ^(2) )^(4)), (you may or may not use reduction formula given)

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

Prove that : int_(0)^(1)x(1-x)^(n)dx=1/((n+1)(n+2))

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

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

Show that int_(0)^(oo) (dx)/((x+sqrt(1+x^(2)))^(n))=(n)/(n^(2)-1), (n in N, n gt 1)