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Chapter 5: Q 27. (page 429)

Solve the integral: $\int x e^{x} d x$

Short Answer

Expert verified

The required answer is $x e^{x} - e^{x} + c$ .

Step by step solution

01

Step 1. Given information.

We have given integral is $\int x e^{x} d x$ .

02

Step 2. Solve the integration by parts .

We have $u = x, d v = e^{x} d x$

The formula of integration by parts is localid="1648636428964" $\int u d v = u v - \int v d u$

$\int x e^{x} d x = x e^{x} - \int e^{x} d x = x e^{x} - e^{x} + c$

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Most popular questions from this chapter

Solve the integral: $\int \frac{3 x + 1}{s e c x} d x$

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Solve $\int \frac{x}{4 + x^{2}} d x$ the following two ways:

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