(x² + 1) x - NCERT Class XII Mathematics Chapter -

NCERT Class XII Mathematics Chapter - - Solutions

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

Question : 148 of 271

Marks: +1, -0

(x^2 + 1) \log x

Solution:

Let

I=\int (x^2 + 1) \log x dx

=\int \log x \cdot (x^2+1)dx

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

=\log x \cdot \left( \frac{x^3}{3} + x \right) - \int \frac{1}{x} \left( \frac{x^3}{3} + x \right) dx + C

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

=\left( \frac{x^3}{3} + x \right) \log x - \frac{x^2}{9} - x + C

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