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Need solution for RD Sharma Maths Class 12 Chapter 18 Indefiite Integrals Excercise Fill in the Blanks Question 15

Answers (1)

Answer:

\frac{-1}{6} e^{-3 x^{2}}+c

Hint:

Simplify it and integrate it.

Solution:

I=\int \frac{x}{e^{3 x^{2}}} d x

Letx^{2} =y           …(i)

\begin{aligned} &\Rightarrow 2 x d x=d y \\ &x d x=\frac{d y}{2} \\ &\Rightarrow I=\frac{1}{2} \int \frac{d y}{e^{3 y}} \end{aligned}

\begin{aligned} &I=\frac{1}{2} \int e^{-3 y} d y \\ &I=\frac{1}{2}\left(\frac{e^{-3 y}}{-3}\right)+c \end{aligned}

 

 I=-\frac{e^{-3 x^{2}}}{6}+c         using…(i)

 

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