Evaluate `int e^xln(x)dx`

Evaluate int x*e^(x)dx

Evaluate int e^x/log(e^x)dx

Evaluate: "int e^(x)a^(x)dx

Evaluate: inte^x/(e^x+2)dx

Evaluate: int x^(3)e^(x)dx

Evaluate int log_e(a^x)dx

Evaluate int_2^3 e^(-x) dx

If u and v are two functions of x then prove that : int uv dx = u int v dx - int [ (du)/(dx) int v dx ] dx Hence, evaluate int x e^(x) dx

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

int xln(a)dx