Engineering Tables/Table of Integrals

This is a small summary of the identities found Here.

	Integral	Value
1	$\int cdx$	$cx+C$
2	$\int x^{n}dx$	$\frac{x^{n+1}}{n+1}+C$Template:Spaces for $n\ne -1$
3	$\int \frac{1}{x}dx$	$\ln \left|x\right|+C$
4	$\int \frac{1}{a^2+x^2}dx$	$\frac{1}{a}\arctan \frac{x}{a}+C$
5	$\int \frac{1}{\sqrt{a^2-x^2}}dx$	$\arcsin \frac{x}{a}+C$
6	$\int \frac{-1}{\sqrt{a^2-x^2}}dx$	$\arccos \frac{x}{a}+C$
7	$\int \frac{1}{x\sqrt{x^2-a^2}}dx$	$\frac{1}{a}\mathrm{arcsec}\frac{|x|}{a}+C$
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	$\int \mathrm{csch}xdx$	$\ln |\tanh \frac{x}{2}|+C$
31	$\int \text{sech}xdx$	$\arctan (\sinh x)+C$
32	$\int \coth xdx$	$\ln |\sinh x|+C$