Important: The student package has been deprecated. Use the superseding commands, Student[Calculus1][IntRules] and Student[Calculus1][Rule], instead.

Carry out integration by parts on an unevaluated integral (expressed in terms of Int).

The function returns $uv-\int \mathrm{du}v\ⅆx$ as its value.

The command with(student,intparts) allows the use of the abbreviated form of this command.

$\mathrm{with}\left(\mathrm{student}\right)\:$

$\mathrm{intparts}\left(\mathrm{Int}\left(x^k\ln \left(x\right)\,x\right)\,\ln \left(x\right)\right)$

$\frac{\ln \left(x\right)x^{k+1}}{k+1}-\int \frac{x^{k+1}}{x\left(k+1\right)}\ⅆx$

$\mathrm{intparts}\left(\mathrm{Int}\left(\sin \left(x\right)x+\sin \left(x\right)\,x\right)\,\sin \left(x\right)\right)$

$\sin \left(x\right)\left(x+\frac{1}{2}{x}^2\right)-\int \cos \left(x\right)\left(x+\frac{1}{2}{x}^2\right)\ⅆx$