Engineering Tables/Properties of Integrals
Table of Properties of Integrals | ||||||||||||
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Rule | Conditions | |||||||||||
1 | ||||||||||||
2 Homogeniety |
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3 Associativity |
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4 Integration by Parts |
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4 General Integration by Parts |
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5 | ||||||||||||
6 Substitution Rule |
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7 |
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8 | ||||||||||||
9 | ||||||||||||
10 | ||||||||||||
Notes: |
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Table of Properties of Integrals | ||||||||||||
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Rule | Conditions | |||||||||||
1 | $\int a\,dx=ax$ | |||||||||||
2 Homogeniety |
$\int af(x)\,dx=a\int f(x)\,dx$ | |||||||||||
3 Associativity |
$\int {\left(f\pm g\pm h\pm \cdots \right)\,dx}=\int f\,dx\pm \int g\,dx\pm \int h\,dx\pm \cdots$ | |||||||||||
4 Integration by Parts |
$\int _{a}^{b}fg'\,dx=\left[fg\right]_{a}^{b}-\int _{a}^{b}gf'\,dx$ | |||||||||||
4 General Integration by Parts |
$\int f^{(n)}g\,dx=f^{(n-1)}g'-f^{(n-2)}g''+\ldots +(-1)^{n}\int fg^{(n)}\,dx$ | |||||||||||
5 | $\int f(ax)\,dx={\frac {1}{a}}\int f(x)\,dx$ | |||||||||||
6 Substitution Rule |
$\int g\{f(x)\}\,dx=\int g(u){\frac {dx}{du}}\,du=\int {\frac {g(u)}{f'(x)}}\,du$ | $u=f(x)\,$ | ||||||||||
7 |
$\int x^{n}\,dx={\frac {x^{n+1}}{n+1}}$ | $n\neq -1\,$ | ||||||||||
8 | $\int {\frac {1}{x}}\,dx=\ln |x|$ | |||||||||||
9 | $\int e^{x}\,dx=e^{x}$ | |||||||||||
10 | $\int a^{x}\,dx={\frac {a^{x}}{\ln |a|}}$ | $a\neq 1$ | ||||||||||
Notes: |
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