x² x - NCERT Class XII Mathematics Chapter - - Solutions

NCERT Class XII Mathematics Chapter - - Solutions

Exercise - 7.6
Integrate the functions in Exercises 134 to 155.

Question : 139 of 271

Marks: +1, -0

x^2 \log x

Solution:

Let

I = \int x^2 \log x \,dx

= \log x \left( \frac{x^3}{3} \right) - \int \left( \left( \frac{d}{dx} \log x \right) \left( \frac{x^3}{3} \right) \right) dx

= \frac{x^3}{3} \log x - \frac{1}{3} \int x^2 \,dx

= \frac{x^3}{3} \log x - \frac{1}{3} \times \frac{x^3}{3} + C

= \frac{x^3}{3} \log x - \frac{x^3}{9} + C

Go to Question: