If `int(dx)/(sqrt(x)(1+x))=mtan^(-1)(x^n),` prove that `m*n=1`

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

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

If int(cosx)/(9-cos^(2)x)dx=m.tan^(-1)[m.f(x)]+c, then

If I_(n)=int(x^(n)dx)/(sqrt(x^(2)+a)) then prove that I_(n)+(n-1)/(n)al_(n-2)=(1)/(n)x^(n-1)*sqrt(x^(2)+a)

If sqrt(1-x^(2n))+sqrt(1-y^(2n))=a^(n)(x^(n)-y^(n)) prove that y^(n-1)*sqrt(1-x^(2n))dy=x^(n-1)sqrt(1-y^(2n))dx

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

int(sqrt(1+x^2)-x)^n dx

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

(b) int(x^(n-1)dx)/(sqrt(a^n+x^n))