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Section8_1_review

# Section8_1_review - Section 8.1 Integration by Parts...

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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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