Evaluate `int_(-1)^(1)5x^(4)sqrt(x^(5)+1)dx`

Evaluate: int_(0)^(1) dx/ sqrt(1 - x^(2))

int_(-1)^(1) log (x+sqrt(x^(2)+1))dx =

Evaluate int (x cos^(-1)x)/(sqrt(1-x^(2))dx

Evaluate : int_(0)^(1)x(1-x)^(n)dx

Evaluate : int(xcos^(-1)x)/(sqrt(1-x^(2)))dx

Evaluate int _(-1)^(1) (x^(3)+5x+ sin x) d x

Prove that int_(-a)^(a) dx = {(2int_(0)^(a) f(x) dx, if f(x) "is even"),(0, if f(x) "is odd"):} and hence evaluate (a) int_(-1)^(1) sin^(5)x cos^(4)xdx .

Evaluate: int_0^(1/2)(xsin^(-1)x)/(sqrt(1-x^2))dx