Engineering Tables/Table of Integrals

From Wikibooks, open books for an open world
< Engineering Tables
Jump to: navigation, search


This is a small summary of the identities found Here.

  Integral Value Remarks
1 \int c \,dx cx+C\,
2 \int x^n\,dx \frac{x^{n+1}}{n+1}+C n \ne -1
3 \int \frac{1}{x}\,dx \ln{\left|x\right|}+C
4 \int {1 \over {a^2+x^2}} \,dx {1 \over a}\arctan {x \over a} + C
5 \int {1 \over \sqrt{a^2-x^2}} \,dx \arcsin {x \over a} + C
6 \int {-1 \over \sqrt{a^2-x^2}} \,dx \arccos {x \over a} + C
7 \int {1 \over x\sqrt{x^2-a^2}} \,dx {1 \over a}\mbox{arcsec}\,{|x| \over a} + C
8 \int \ln {x}\,dx x \ln {x} - x + C \,
9 \int \log_b {x}\,dx 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{x}\, dx -\cos{x} + C\,
13 \int \cos{x}\, dx \sin{x} + C\,
14 \int \tan{x} \, dx -\ln{\left| \cos {x} \right|} + C\,
15 \int \cot{x} \, dx \ln{\left| \sin{x} \right|} + C\,
16 \int \sec{x} \, dx \ln{\left| \sec{x} + \tan{x}\right|} + C\,
17 \int \csc{x} \, dx -\ln{\left| \csc{x} + \cot{x}\right|} + C\,
18 \int \sec^2 x \, dx \tan x + C\,
19 \int \csc^2 x \, dx -\cot x + C\,
20 \int \sec{x} \, \tan{x} \, dx \sec{x} + C\,
21 \int \csc{x} \, \cot{x} \, dx - \csc{x} + C\,
22 \int \sin^2 x \, dx \frac{1}{2}(x - \sin x \cos x) + C\,
23 \int \cos^2 x \, dx \frac{1}{2}(x + \sin x \cos x) + C\,
24 \int \sin^n x \, dx - \frac{\sin^{n-1} {x} \cos {x}}{n} + \frac{n-1}{n} \int \sin^{n-2}{x} \, dx
25 \int \cos^n x \, dx - \frac{\cos^{n-1} {x} \sin {x}}{n} + \frac{n-1}{n} \int \cos^{n-2}{x} \, dx
26 \int \arctan{x} \, dx x \, \arctan{x} - \frac{1}{2} \ln{\left| 1 + x^2\right|} + C
27 \int \sinh x \, dx \cosh x + C\,
28 \int \cosh x \, dx \sinh x + C\,
29 \int \tanh x \, dx \ln |\cosh x| + C\,
30 \int \mbox{csch}\,x \, dx \ln\left| \tanh {x \over2}\right| + C
31 \int \mbox{sech}\,x \, dx \arctan(\sinh x) + C\,
32 \int \coth x \, dx \ln|\sinh x| + C\,