int(3x^(8)+2x^(2)+3n+1)/(3(n^(2)+1))dn

int_(2)^(4) (3x^(2)+1)/((x^(2)-1)^(3))dx = (lambda)/(n^(2)) where lambda, n in N and gcd(lambda,n) = 1 , then find the value of lambda + n

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

int(n^(4))/((n-1)(n^(2)+1))dn

int_ (2) ^ (3) (n) / (1 + n ^ (2)) dn

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

The coefficient of x^(n) in (1-(x)/(1!)+(x^(2))/(2!)-(x^(3))/(3!)+...+((-1)^(n)x^(n))/(n!))^(2) is equal to

int_0^1 (2x^2-3)^n xdx

int_0^1 (2x^2-3)^n xdx