x 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 : 137 of 271

Marks: +1, -0

x \log x

Solution:

Let

I=\int x \log x dx

=\log x \int x dx - \int \left[ \frac{d}{dx}(\log x) \int x dx \right] dx

=\log x \left( \frac{x^2}{2} \right) - \int \left( \frac{1}{x} \cdot \frac{x^2}{2} \right) dx

=\frac{x^2}{2} \log x - \frac{1}{2} \int x dx + C

=\frac{x^2}{2} \log x - \frac{1}{2} \times \frac{x^2}{2} + C

=\frac{x^2}{2} \log x - \frac{1}{4} x^2 + C

Go to Question: