Difference between revisions of "Integration by parts"
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The rule for '''integration by parts''' is stated as follows: | The rule for '''integration by parts''' is stated as follows: | ||
| − | :<big><big><big><math>\int f(x) g'(x)\,dx = f(x) g(x) - \int f'(x) g(x)\,dx,</math></big></big> | + | :<big><big><big><math>\int f(x) g'(x)\,dx = f(x) g(x) - \int f'(x) g(x)\,dx,</math></big></big></big> |
| − | This rule is often useful when one function is a | + | This rule is often useful when one function is a power of ''x'' and the other function is a trigonometric function or ''e'' raised to a power of ''x''. |
| + | Note that it may be necessary to repeat the '''integration by parts''' several times, one for each power of ''x''. | ||
[[category:mathematics]] | [[category:mathematics]] | ||
[[category:calculus]] | [[category:calculus]] | ||
Revision as of 05:09, November 26, 2007
Integration by parts is a special technique to facilitate the integration of the product of two functions that otherwise lack an obvious integral. This technique utilizes the insight of the product rule or chain rule.
The rule for integration by parts is stated as follows:
- <math>\int f(x) g'(x)\,dx = f(x) g(x) - \int f'(x) g(x)\,dx,</math>
This rule is often useful when one function is a power of x and the other function is a trigonometric function or e raised to a power of x.
Note that it may be necessary to repeat the integration by parts several times, one for each power of x.