\textbf{Integration table}

Exponents and Powers (special case for \[x\] is obtained by setting \[a=1, b=0\])
\begin{tabular*}
\[\int (ax + b)\ \mathrm{d}x = a\frac{x^2}{2} + bx + C\] & \[\int (ax + b)^n\ \mathrm{d}x = \frac{1}{a}\cdot \frac{(ax+b)^{n + 1}}{n + 1} + C\ (n\neq -1)\]\\
\[\int\frac{\mathrm{d}x}{ax + b} = \frac{1}{a}\ln|ax + b| + C\] & \[\int e^{ax + b}\mathrm{d}x = \frac{e^b}{a}\cdot e^{ax+b} + C\] 
\end{tabular*}
Trigonometric:

\begin{tabular*}
\[\int\sin(\omega x)\mathrm{d}x = -\frac{1}{\omega}\cos(x) + C\] & \[\int\cos(\omega x)\mathrm{d}x = \frac{1}{\omega}\sin(x) + C\] & \[\int\tan(\omega x)\mathrm{d}x = \frac{1}{\omega}\ln\left|\frac{1}{\cos(x)}\right| + C\]\\
\[\int\frac{\mathrm{d}x}{\sin^2(\omega x)} = -\frac{1}{\omega}\cot(\omega x) + C\] & 
\[\int\frac{\mathrm{d}x}{\cos^2(\omega x)} = \frac{1}{\omega}\tan(\omega x) + C\]
\end{tabular*}
Hyperbolic:

\begin{tabular*}
\[\int\sinh(x)\mathrm{d}x = \cosh(x) + C\] & \[\int\cosh(x)\mathrm{d}x = \sinh(x) + C\]
& \[\int\tanh(x)\mathrm{d}x =\ln\cosh(x) + C\]\\
\[\int\frac{\mathrm{d}x}{\sinh^2(x)} = -\coth(x) + C\] & 
\[\int\frac{\mathrm{d}x}{\cosh^2(x)} = \tanh(x) + C\]
\end{tabular*}

Inverse quadratic:

\begin{tabular*}
\[\int\frac{\mathrm{d}x}{x^2 + a^2} = \frac{1}{a}\arctan\left(\frac{x}{a}\right) + C\]
&\[\int\frac{\mathrm{d}x}{x^2 - a^2}=\frac{1}{2a}\ln\left|\frac{x - a}{x + a}\right| +C\]
&\[\int\frac{\mathrm{d}x}{a^2 - x^2} = \frac{1}{2a}\ln\left|\frac{a+x}{a-x}\right| + C\]
\\
\[\int\frac{\mathrm{d}x}{\sqrt{x^2 + a^2}} = \ln\left|x + \sqrt{x^2 + a^2}\right| + C\]&
\[\int\frac{\mathrm{d}x}{\sqrt{x^2 - a^2}} = \ln\left|x + \sqrt{x^2 - a^2}\right| + C\]
&\[\int\frac{\mathrm{d}x}{\sqrt{a^2 - x^2}} = \arcsin\left(\frac{x}{a}\right) + C\]
\end{tabular*}