`int(9x^(n))/(x^(n+1)+b)dx`

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

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

int(x^(n-1))/(sqrt(1+4x^(n)))dx

int_(n in N)(a*x^(n-1))/(bx^(n)+c)dx where a,b,c are real nuber

If int_(a)^(b) (x^(n))/(x^(n)+(16-x)^(n))dx=6 , then

U_(n)=int_(0)^(1)x^(n)(2-x)^(n)dx and V_(n)=int_(0)^(1)x^(n)(1-x)^(n)dx,n in N and if (V_(n))/(U_(n))=1024, then the value of n is

If I(m,n)=int_(0)^(1)x^(m-1)(1-x)^(n-1)dx,(m,n in I,m,n>=0),th epsilonI(m,n)=int_(0)^(oo)(x^(m-1))/((1+x)^(m-n))dxI(m,n)=int_(0)^(oo)(x^(m-1))/((1+x)^(m+n))dxI(m,n)=int_(0)^(oo)(x^(n-1))/((1+x)^(m+n))dxI(m,n)=int_(0)^(oo)(x^(n))/((1+x)^(m+n))dx

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)