`underset(2)overset(3)int (2x)/(1+x^(2))dx`

Evaluate the following definite integrals underset(0)overset(1)int(dx)/(sqrt(1-x^(2)))

Evaluate the following definite integrals underset(0)overset(a)int(x)/(sqrt(a^(2)+x^(2)))dx

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

underset(1)overset(e)int (e^(x))/(x) (1 + x log x)dx

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

Evaluate the following definite integrals underset(0)overset(pi//4)int(dx)/(1+cos2x)

If f(x)={{:(x,xlt1),(x-1,xge1):} , then underset(0)overset(2)intx^(2)f(x) dx is equal to :

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

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

Let [t] denote the greatest integer le t. Then the value of 8 underset(-1/2)overset(1)int [2x]+|x| dx is ____________