student(deprecated)/intparts - Maple Help

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student

 intparts
 perform integration by parts

 Calling Sequence intparts(f, u)

Parameters

 f - expression of the form Int(u*dv, x) u - factor of the integrand to be differentiated

Description

 • 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 $uv-\left({\int }\mathrm{du}v\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{ⅆ}x\right)$ as its value.
 • The command with(student,intparts) allows the use of the abbreviated form of this command.

Examples

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

 > $\mathrm{with}\left(\mathrm{student}\right):$
 > $\mathrm{intparts}\left(\mathrm{Int}\left({x}^{k}\mathrm{ln}\left(x\right),x\right),\mathrm{ln}\left(x\right)\right)$
 $\frac{{\mathrm{ln}}{}\left({x}\right){}{{x}}^{{k}{+}{1}}}{{k}{+}{1}}{-}\left({\int }\frac{{{x}}^{{k}{+}{1}}}{{x}{}\left({k}{+}{1}\right)}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{ⅆ}{x}\right)$ (1)
 > $\mathrm{intparts}\left(\mathrm{Int}\left(\mathrm{sin}\left(x\right)x+\mathrm{sin}\left(x\right),x\right),\mathrm{sin}\left(x\right)\right)$
 ${\mathrm{sin}}{}\left({x}\right){}\left(\frac{{1}}{{2}}{}{{x}}^{{2}}{+}{x}\right){-}\left({\int }{\mathrm{cos}}{}\left({x}\right){}\left(\frac{{1}}{{2}}{}{{x}}^{{2}}{+}{x}\right)\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{ⅆ}{x}\right)$ (2)

 See Also