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Integration by Parts

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rebelmaths

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Use Integration by Parts

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Integration by Parts

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Evaluate $\\int_0^\\pi x \\cos(x) \\mathrm{dx}$ using integration by parts, letting $u = x$ and $\\mathrm{dv} = \\cos(x)$

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Evaluate $\\int_1^\\var{b}x^\\var{a}\\ln(x)\\mathrm{dx}$ using integration by parts, letting $u = \\ln(x)$ and $\\mathrm{dv} = x^\\var{a}$.

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Evaluate $\\int_0^{1/2}x\\cos(x)\\mathrm{dx}$ using the substitution $u = x$ and $\\mathrm{dv} = \\cos(\\pi x)\\mathrm{dx}$.
When writing $\\pi$ in your answer simly write pi.