Find `underset(-a)overset(a)int x^(2) (a^(2)-x^(2))^(3//2)dx`

underset1overset2int 3x^2dx =???

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

Evaluate: int(x^(2))/((a^(2)-x^(2))^(3/2))dx

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

If the value definite integral underset(-4)overset(4)(f)(x^(3)-2x^(2)-"cosec"^(3)x+tanx)/(5-|x|)dx=a+bln5,"where "a,binI , find the value of ((a+b)/(2)) .

Find: int x^(2)(x^(5)+2x^(3))dx

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

Evaluate : int(2-x^(2))^(3)dx

Evaluate int(x^(3))/(x^(4)-x^(2)-2)dx

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