$\int a^x \, da = $

$\int \sqrt{1 + \cos x} \, dx$ equals

Find the following integral: $\int \frac{x^{3}+5 x^{2}-4}{x^{2}} d x$

Let $f(x) = \tan^{-1}\left(\frac{1+\cos x}{\sin x}\right)$ and $g(x) = \tan^{-1}\left(\frac{\sin x}{1-\cos x}\right)$. Then,evaluate $\int (f(x) + g(x)) \, dx$.

$\int \frac{dx}{x^2 + 4x + 13}$ is equal to

The integral of $\frac{x^2 - x}{x^3 - x^2 + x - 1}$ with respect to $x$ is: