{e^{^{-1}x}}{1+x² - NCERT Class XII Mathematics Chapter -

NCERT Class XII Mathematics Chapter - - Solutions

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

Question : 40 of 271

Marks: +1, -0

\frac{e^{\tan^{-1}x}}{1+x^2}

Solution:

Let

I = \int \frac{e^{\tan^{-1}x}}{1+x^2}dx

Put

\tan^{-1}x = t

\Rightarrow \frac{1}{1+x^2}dx = dt

\therefore I = \int e^t dt = e^t + C

= e^{\tan^{-1}x} + C

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