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Calculus 2: Integration by Parts

Evaluate x2cos(x)dx\int x^2 \, cos(x) \, dx

Evaluate xsin(x)dx\int x \, sin(x) \, dx

Evaluate x4ln3xdx\int x^4 \, ln \, 3x \, dx

Evaluate sin(1x)x3dx\displaystyle \int \frac{sin(\frac{1}{x})}{x^3} \, dx

Evaluate tan1xdx\displaystyle \int tan^{-1} \, \sqrt{x} \, dx

Evaluate 5xe2xdx\displaystyle \int \frac{5x}{e^{2x}} \, dx

Compute xe5xdx\int xe^{5x}dx and π/4π/3cos(x)ln(sin(x))dx\displaystyle \int_{\pi/4}^{\pi/3} cos(x) ln(sin(x)) \, dx