Evaluate `int e^(7x).dx`

Evaluate int e^xln(x)dx

Evaluate int x*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

int e^(2x+7)dx

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

(f) Evaluate int(7)/(1+x)dx

Evaluate: (i) int xe^(x)^^2dx (ii) int(e^(2x))/(1+e^(x))dx

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

Evaluate: int e^(x)sqrt(e^(2x)+1)dx

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