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Integration by parts

  • Thread starter jpd5184
  • Start date
  • #1
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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)
 

Answers and Replies

  • #2
33,484
5,174

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.
[tex]\int x^2 ln(x)dx = \frac{x^3}{3}ln(x) - \frac{1}{3}\int \frac{x^3}{x} dx + C[/tex]
 
  • #3
dextercioby
Science Advisor
Homework Helper
Insights Author
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The natural logarithm is also a function recognized by LaTeX. It has the code [itex] \ln x [/itex]. Its inverse, the exponential function in the base e also has a code [itex] \exp x [/itex].
 

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