`int_-2^2(1/(1+sqrte^x))dx`

Evaluate: int_(0)^(4)(1)/(x+sqrt(x))dx( ii) int_(0)^(1)(2x)/(5x^(2)+1)dx

int_(-1)^(1)(x)/(sqrt(a^(2)-x^(2)))dx(a>1)

int_(1)^(2)(1)/(x sqrt(x^(2)-1))dx=

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

show that (a) int_(0) ^(2pi) sin ^(3) x dx = 0 , (b) int_(-1)^(1) e^(-x^(2)) dx = 2 int_(0)^(1) e^(-x^(2)) dx

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

int_(1/2)^(1)(1)/(sqrt(1-x^(2)))dx=

int_(1)^(2)((x+1)^(2))/(sqrt(x))dx

int_(1)^(2)((x+1)^(2))/(sqrt(x))dx

int_(-1)^1(dx)/(1+x^2)