1/x ( x)^m, x > 0 - NCERT Class XII Mathematics Chapter -

NCERT Class XII Mathematics Chapter - - Solutions

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

Question : 36 of 271

Marks: +1, -0

\frac{1}{x (\log x)^m}, x > 0

Solution:

Let

I = \frac{1}{x (\log x)^m} dx, x > 0

Put

\log x = t

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

\therefore I = \int \frac{dt}{t^m} = \int t^{-m} dt = \frac{t^{-m+1}}{-m+1} + C

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

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