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Integrals / Integration by Parts (9 questions)

QuestionAnswer
$\int x \ln(x) dx$ $\frac{x^2}{2}(\ln(x) - \frac{1}{2})+C$
$\int x \sin(x) dx$ $\sin(x) - x \cos(x) + C$
$\int x \cos(x) dx$ $\cos(x) + x \sin(x)$
$\int x \cos(x) dx$ $\cos(x) + x \sin(x) +C$
$\int x e^{x} dx$ $xe^x - e^x + C$
$\int 3 x^2 \ln(x) dx$ $x^3 \ln(x) - \frac{x^3}{3} + C$
$\int \frac{x}{e^{3x}}dx$ $\frac{-x}{3 e^{3x}} - \frac{1}{9e^{3x}}$
$\int \frac{x}{e^x}dx$ $\frac{-x}{e^x} - \frac{1}{e^x}$
$\int x \sin(\pi x) dx$ $\frac{\sin(\pi x) - \pi x \cos(\pi x)}{\pi^2} + C$