Question

$$\text { Integration by parts Evaluate the following integrals.}$$ $$\int x^{2} \ln x^{3} d x$$

   $$\text { Integration by parts Evaluate the following integrals.}$$
$$\int x^{2} \ln x^{3} d x$$

Calculus for Scientists and Engineers: Early Transcendental

William Briggs, Lyle… 1st Edition

Chapter 7, Problem 13

Instant Answer

Solved by Expert Robert Daugherty

06/02/2020

Step 1

We let $u = \ln x^{3}$ and $dv = x^{2} dx$. Show more…

Show all steps

Thanks for your feedback!

$$\text { Integration by parts Evaluate the following integrals.}$$ $$\int x^{2} \ln x^{3} d x$$

Play audio

Feedback

Robert Daugherty and 84 other subject Calculus 1 / AB educators are ready to help you.

Ask a new question

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Integration by Parts

This is a technique used in calculus to integrate products of functions. It is based on the product rule for differentiation and allows one to convert a complicated integral into simpler parts by choosing one function to differentiate (u) and another to integrate (dv), using the formula ?u dv = uv - ?v du.

Properties of Logarithms

Properties of logarithms, such as the rule ln(a^b) = b ln a, are fundamental for simplifying integrals that involve logarithmic expressions. This particular property lets you take exponents in the argument of a logarithm out as multipliers, which often simplifies the integrals and makes them easier to handle with methods like integration by parts.

Please give Ace some feedback