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

NCERT Class XII Mathematics Chapter - - Solutions

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

Question : 39 of 271

Marks: +1, -0

\frac{x}{e^{x^2}}

Solution:

Let

I=\int \frac{x}{e^{x^2}}\,dx

Put

x^2 = t

\Rightarrow 2x\,dx = dt

\therefore I=\frac{1}{2}\int\frac{dt}{e^t}=\frac{1}{2}\int e^{-t}\,dt

=\frac{1}{2}\left(\frac{e^{-t}}{-1}\right)+C

=-\frac{1}{2e^t}+C

=-\frac{1}{2e^{x^2}}+C

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