`int_(1)^(2)((2x+5)/(3))dx`

int_(1)^(2)x^(5)dx

If I_(1)=int_(0)^(1) 2^(x^(2)) dx, I_(2)=int_(0)^(1) 2^(x^(3)) dx, I_(3)=int_(1)^(2) 2^(x^(2))dx and I_(4)=int_(1)^(2) 2^(x^(3))dx then

int_(0)^(1)x^(2)(1-x)^(3)dx is equal to

int_(1)^(2) (x^3+1) dx

int_(1)^(9)(x^((3)/(2))+2x+3)dx

Evaluate int_(1)^(3)(x^(2)-2x)dx

Evaluate : (i) int_(-oo)^(oo) (dx)/(x^(2)+2x+2) , (ii) int_(sqrt(2))^(oo)(dx)/(xsqrt(x^(2)-1)) , (iii) int_(0)^(4)(x^(2))/(1+x)dx (iv) int_(0)^(pi//2) sqrt(costheta)sin^(3)theta

Let I_(1)=int_(1)^(2)(x)/(sqrt(1+x^(2)))dx and I_(2)=int_(1)^(2)(1)/(x)dx .Then

int_(1)^(5) (x^(2) -2x) dx

int_(0)^(3)(x^(2)+1)dx