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Unformatted text preview: Section 8.1: Integration by Parts Integration by parts formula for an indefinite integral: udv = uv- vdu Integration by parts formula for a definite integral: udv a b = uv a b- vdu a b Notes: Choose u and dv. (Everything within the original integral is accounted for by these choices.) Differentiate u to obtain du . Integrate dv to obtain v . u is generally chosen so that it becomes simpler when differentiated, or at least not more complicated, and it must be possible to integrate dv . Although there are exceptions, integration by parts is generally used when the integrand contains a power of x (or a polynomial) in combination with a trigonometric function, an exponential function, or a logarithmic function. For the case with a power of x (or a polynomial) occurring with a trigonometric function, let u be the power of x (or the polynomial) and dv be the trigonometric function times dx ....
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