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→Integration by Parts
===Integration by Parts===
===Integration by Parts===
'''Integration by parts''' is a special [[Techniques of integration|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]].
The rule for '''integration by parts''' is stated as follows:
:<big><math>\int f(x) g'(x)\,dx = f(x) g(x) - \int f'(x) g(x)\,dx,</math></big>
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''.
===Partial Fractions===
===Partial Fractions===
===Algebraic Substitution===
===Algebraic Substitution===
===Trigonometric Substitution===
===Trigonometric Substitution===