How can integration by parts be used to solve this integral?

[jpd5184]

Homework Statement

integral of x^2ln(x)dx

Homework Equations

The Attempt at a Solution

u=ln(x)
du= 1/x
dv=x2dx
x^3/3

integral x^2ln(x)dx = ln(x)x^3/3-intergral(x^3/3)(1/x)

 

[Mark44]

Homework Statement

integral of x^2ln(x)dx

Homework Equations

The Attempt at a Solution

u=ln(x)
du= 1/x
dv=x2dx
x^3/3

integral x^2ln(x)dx = ln(x)x^3/3-intergral(x^3/3)(1/x)

You're on the right path. Just continue what you're doing, but simplify the integrand on the right. Don't forget dx or the constant of integration, though.

Here's the work in LaTeX. Click the equation to see what I did.
$$\int x^2 ln(x)dx = \frac{x^3}{3}ln(x) - \frac{1}{3}\int \frac{x^3}{x} dx + C$$

 

[dextercioby]

The natural logarithm is also a function recognized by LaTeX. It has the code $\ln x$. Its inverse, the exponential function in the base e also has a code $\exp x$.