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Integration by Parts worksheet with six problems and substitution hints.

Worksheet titled "Integration by Parts" with six calculus problems requiring indefinite integrals using substitution, each with u and dv provided.

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1) $ e^x \sin(x) - \int e^x \cos(x) dx $
2) $ x^2 \cdot \frac{e^{4x}}{4} - \int 2x \cdot \frac{e^{4x}}{4} dx $
3) $ \ln(x) \cdot \ln|x| - \int \frac{1}{x} \cdot \ln|x| dx $
4) $ x^2 \cdot \left(-\frac{\cos(10x)}{10}\right) - \int 2x \cdot \left(-\frac{\cos(10x)}{10}\right) dx $
5) $ x^3 \cdot \frac{2}{3}(x^3 + 9)^{3/2} - \int 3x^2 \cdot \frac{2}{3}(x^3 + 9)^{3/2} dx $
6) $ x \cdot \frac{2}{3}(x + 2)^{3/2} - \int 1 \cdot \frac{2}{3}(x + 2)^{3/2} dx $

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