Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa

Evaluate the integral of  x^{5}log^{2}x

Option: 1

\frac{x^{6}log^{2}x}{6}+\frac{x^{6}log\ x}{18}+\frac{x^{6}}{108}+C


Option: 2

\frac{x^{6}log^{2}x}{6}-\frac{x^{6}log\ x}{18}+\frac{x^{6}}{108}+C


Option: 3

\frac{x^{6}log^{2}x}{6}-\frac{x^{6}log\ x}{18}-\frac{x^{6}}{108}+C


Option: 4

-\frac{x^{6}log^{2}x}{6}-\frac{x^{6}log\ x}{18}+\frac{x^{6}}{108}+C


Answers (1)

best_answer

Given integral, 
\int x^{5}log^{2}x\ dx
The reduction formula used is,
\int x^{n}log^{m}x\ dx=\frac{x^{n+1}log^{m}x}{n+1}-\frac{m}{n+1}\int x^{n}log^{m-1}x\ dx

\int x^{5}log^{2}x\ dx=\frac{x^{6}log^{2}x}{6}-\frac{2}{6}\int x^{5}log\ x\ dx
\int x^{5}log^{2}x\ dx=\frac{x^{6}log^{2}x}{6}-\frac{1}{3}\left ( \frac{x^{6}log\ x}{6}-\frac{1}{6}\int x^{5}\ dx \right )
\int x^{5}log^{2}x\ dx=\frac{x^{6}log^{2}x}{6}-\frac{x^{6}log\ x}{18}+\frac{x^{6}}{108}+C

Posted by

Shailly goel

View full answer

JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE

Similar Questions

Trending Articles/News

anam-khan

BTech Admissions 2025 LIVE: JEE Main, MET registration underway; how to apply
anam-khan

JEE Main 2025 Registration: NTA issues advisory for Aadhaar authentication, name mismatch issues
anam-khan

BTech Admissions 2025: JEE Main registration last date, direct link

Latest Question