Slide 7.1.pptx - Integration by Parts Integration by Parts...

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Integration by Parts
Integration by Parts Let’s learn how to evaluate integrals of functions such as ln(x), xe x , x 2 cos(x) and more… [f(x)g(x)]’ = f(x)g’(x) + g(x)f’(x) ∫f(x)g’(x)dx = ∫[f(x)g(x)]’dx - ∫g(x)f’(x)dx = f(x)g(x) - ∫g(x)f’(x)dx
Selecting u and dv Rules for choosing u and dv: For dv: Choose the most complicated integrand that can be readily integrated. For u: Choose something that becomes simpler when differentiated *Tip: Choose u based on which of these comes first: I (inverse trigonometric), L (logarithmic), A (algebraic), T (trigonometric), E (exponential).
Example 1 Evaluate u = x → du = dx dv = e 3x dx → v = e

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