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 $uv-\left(\int \mathrm{du}v\ⅆx\right)$ as its value.

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

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

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

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

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

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