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

NCERT Class XII Mathematics Chapter - - Solutions

Exercise - 7.2
Integrate the functions in Exercises 23 to 59.

Question : 58 of 271

Marks: +1, -0

\frac{(x+1)(x+\log x)}{x}

Solution:

Let

I=\int \frac{(x+1)(x+\log x)}{x} dx

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

Put

x+\log x = t

\Rightarrow \left(1+\frac{1}{x}\right) dx = dt

\therefore I = \int t^2 dt = \frac{t^3}{3} + C

= \frac{1}{3} (x+\log x)^3 + C

Go to Question: