Engineering Tables/Table of Integrals

This is a small summary of the identities found Here.

	Integral
1	$\int dx=x+C$
2	$\int x^{n}dx=\frac{x^{n+1}}{n+1}+C\text{ if }n\ne -1$
3	$\int \frac{1}{x}dx=\ln \left|x\right|+C$
4	$\int \frac{dx}{a^2+x^2}=\frac{1}{a}\arctan \frac{x}{a}+C$
5	$\int \frac{dx}{\sqrt{a^2-x^2}}=\arcsin \frac{x}{a}+C$
6	$\int \frac{-dx}{\sqrt{a^2-x^2}}=\arccos \frac{x}{a}+C$
7	$\int \frac{dx}{x\sqrt{x^2-a^2}}=\frac{1}{a}\text{arcsec}\frac{|x|}{a}+C$
8	$\int \ln xdx=x\ln x-x+C$
9	$\int {\log }_{b}xdx=x{\log }_{b}x-x{\log }_{b}e+C$
10	$\int e^{x}dx=e^x+C$
11	$\int a^{x}dx=\frac{a^x}{\ln a}+C$
12	$\int \sin xdx=-\cos x+C$
13	$\int \cos xdx=\sin x+C$
14	$\int \tan xdx=-\ln |\cos x|+C$
15	$\int \cot xdx=\ln |\sin x|+C$
16	$\int \sec xdx=\ln |\sec x+\tan x|+C$
17	$\int \csc xdx=-\ln |\csc x+\cot x|+C$
18	$\int {\sec }^{2}xdx=\tan x+C$
19	$\int {\csc }^{2}xdx=-\cot x+C$
20	$\int \sec x\tan xdx=\sec x+C$
21	$\int \csc x\cot xdx=-\csc x+C$
22	$\int {\sin }^{2}xdx=\frac{1}{2}(x-\sin x\cos x)+C$
23	$\int {\cos }^{2}xdx=\frac{1}{2}(x+\sin x\cos x)+C$
24	$\int {\sin }^{n}xdx=-\frac{{\sin }^{n-1}x\cos x}{n}+\frac{n-1}{n}\int {\sin }^{n-2}xdx$
25	$\int {\cos }^{n}xdx=-\frac{{\cos }^{n-1}x\sin x}{n}+\frac{n-1}{n}\int {\cos }^{n-2}xdx$
26	$\int \arctan xdx=x\arctan x-\frac{1}{2}\ln |1+x^2|+C$
27	$\int \sinh xdx=\cosh x+C$
28	$\int \cosh xdx=\sinh x+C$
29	$\int \tanh xdx=\ln |\cosh x|+C$
30	$\int \text{csch}xdx=\ln |\tanh \frac{x}{2}|+C$
31	$\int \text{sech}xdx=\arctan (\sinh x)+C$
32	$\int \coth xdx=\ln |\sinh x|+C$