Integration by Parts

The integration by parts formula states that

$\displaystyle \int$u dv = uv - $\displaystyle \int$v du

$\blacktriangleright$ To use integration by parts on $\int$x ln x dx

1.
Leave the insertion point in the integral.

2.
From the Calculus submenu, choose Integrate by Parts.

3.
Enter ln x (as the Part to be Differentiated) in the dialog box.

4.
Choose OK.

$\blacktriangleright$ Calculus + Integrate by Parts

$\dint$x ln x dx = ${\frac{{1}}{{2}}}$$\left(\vphantom{ \ln x}\right.$ln x$\left.\vphantom{ \ln x}\right)$x2 - $\dint$${\frac{{1}}{{2}}}$x dx

Note that in this case, u = ln x and dv = x dx, so that du = ${\frac{{1}}{{x}%
}}$ dx and v = ${\frac{{1}}{{2}}}$x2.