Evaluate : `int_0^(ln2)x e^(-x)dx`

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

Suppose that f,f^prime and f prime prime are continuous on [0, ln 2] and that f (0) = 0, f prime(0) = 3, f(In 2) = 6,f prime(ln 2) = 4 and int_0^(ln 2) e^(-2x)*f(x)dx=3. Find the value of int_0^(ln2) e^(-2x)*f prime prime(x)dx.

Evaluate :int_(0)^(1)x log(1+2x)dx

Evaluate: int_0^1 (dx)/(e^x+e^(-x))

Evaluate int 2e^(ln x) dx .

Evaluate: int_e^(e^2) (dx)/(x log x)

Evaluate : int e^(3 log x)dx

Evaluate: int_(0)^(e-1)((x^(2)+2x-1)/(2))/(x+1)dx+int_(1)^(e)x log xe^((z^(2)-2)/(2))dx

Evaluate int_0^3 x^2.e^(x^3) dx

int e^(x ln a)*e^(x)dx