{1}{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 : 32 of 271

Marks: +1, -0

\frac{1}{x-\sqrt{x}}

Solution:

Let

I = \int \frac{1}{x-\sqrt{x}} \, dx

= \int \frac{1}{\sqrt{x}(\sqrt{x}-1)} \, dx

Put

\sqrt{x} - 1 = t

\Rightarrow \frac{1}{2\sqrt{x}} dx = dt

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

= 2 \log(\sqrt{x} - 1) + C

Go to Question: