# Integration by parts

## Homework Statement

integral of x^2ln(x)dx

## 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)

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Mark44
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## Homework Statement

integral of x^2ln(x)dx

## 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 $\exp x$.