What is the integral of e^x dx?

Evaluate the integral: $\int \frac{2e^x}{9+4e^{2x}}dx$

Find the indefinite integral.

$\int \frac{e^{4x}}{e^x-1}dx$

What is the integral of \( \frac{1}{x} \, dx \)?

Evaluate the integral \( \int \frac{x}{x^2 + 1} \, dx \) by choosing an appropriate substitution.

Evaluate $\int \frac{dx}{1-\sin x+\cos x}$.

Given the derivative of the inverse tangent function is 1/(1 + x^2), synthesize the integral of 1/(1 + x^2) dx.

Rewrite the integrand 1/(x^2 + 4x + 5) using the method of completing the square.

Evaluate $\int x{\tanh }^{-1}xdx$.