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  • need solution for RD Sharma maths class 12 chapter Indefinite Integrals exercise 18.9 question 59

need solution for RD Sharma maths class 12 chapter Indefinite Integrals exercise 18.9 question 59

Answers (1)

Answer: \frac{1}{2} e^{x^{2}}+c

Hint: Use substitution method to solve this integral

Given: \int x\: e^{x^{2}} d x

Solution:

        \text { Let } I=\int x\: e^{x^{2}} d x

        \begin{aligned} &\text { Put } x^{2}=t \Rightarrow 2 x d x=d t \Rightarrow d x=\frac{1}{2 x} d t \\ &\text { Then, } I=\int x \cdot e^{t} \cdot \frac{d t}{2 x}=\frac{1}{2} \int e^{t} d t=\frac{1}{2} e^{t}+c \end{aligned}                    \left[\because \int e^{x} d x=e^{x}+c\right]

                        =\frac{1}{2} e^{x^{2}}+c                                    \left[\because t=x^{2}\right]

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