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Please Solve R.D.Sharma Class 12 Chapter 18 Indefinite Integrals Exercise 18.25 Question 4 Maths Textbook Solution.

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Answer: x e^{x}-e^{x}+c

Hint: Using integration by parts

         \int u v d x=u \int v d x-\int \frac{d}{d x} u \int v d x

Given: I=\int x e^{x} d x

Solution: I=x \int e^{x} d x-\int \frac{d}{d x} x \int e^{x} d x

  We have,    \int e^{x} d x=e^{x} \& \frac{d}{d x} x=1

                               \begin{aligned} &=x e^{x}-\int e^{x} d x \\ &=x e^{x}-e^{x}+c \end{aligned}


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