Problem

Use integration by parts to prove the reduction f…

01:53

Problem 51 Medium Difficulty

Use integration by parts to prove the reduction formula.

$ \displaystyle \int (\ln x)^n dx = x (\ln x)^n - n \displaystyle \int (\ln x)^{n - 1} dx $

Name: use integration by parts to prove the reduction formula displaystyle int ln xn dx x ln xn n displays
Uploaded: 2018-02-01
Duration: 2 min 1 s
Channel: Numerade
Description: Use integration by parts to prove the reduction formula. $ \displaystyle \int (\ln x)^n dx = x (\ln x)^n - n \displaystyle \int (\ln x)^{n - 1} dx $

Answer

$=x(\ln x)^{n}-n \int(\ln x)^{n-1} d x$

Topics

Integration Techniques

Calculus: Early Transcendentals

Chapter 7

Techniques of Integration

Section 1

Integration by Parts

Discussion

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Video Transcript

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