5*int e^(x)*(x^(3)+x+1)/((1+x^(2))^(3/2))dx

The value of int e^(x)((x^(3)+x+1))/((1+x^(2))^((3)/(2)))dx is

Integrate : int (e^(x)(x^(3)+x+1))/((1+x^(2))^((3)/(2)))dx

Evaluate: int(e^x(x^3+x+1))/(1+x^2)^(3/2)dx

int e^(x)((1)/(x^(2))-(2)/(x^(3)))dx

(3) int(dx)/(1+e^(2x))

" (8) "quad e=int(x+(1)/(x))^(3/2)((x^(2)-1)/(x^(2)))^(dx)

int(x+(1)/(x))^(3/2)((x^(2)-1)/(x^(2)))dx is equal to (A) (1)/(3)(x+(1)/(x))^(3)+C (B)(2)/(5)(x+(1)/(x))^(5/2)

If int f(x)dx=psi(x), then int x^(5)f(x^(3))dxint x^(5)f(x^(3))dx(1)/(3)x^(3)psi(x^(3))-3int x^(3)psi(x^(3))dx+C(2)(1)/(3)x^(3)psi(x^(3))-int x^(3)psi(x^(3))dx+C(3)(1)/(3)x^(3)psi(x^(3))-int x^(3)psi(x^(3))dx+C(4)(1)/(3)[x^(3)psi(x^(3))-int x^(2)psi(x^(3))dx]+C

int_(-3)^(3)(x^(2))/((x^(2)+3)(1+e^(x)))dx is equal to

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