Book edition 1st

Author(s) Peter Kohn, Laura Taalman

Pages 1155 pages

ISBN 9781429241861

Answers without the blur.

Just sign up for free and you're in.

Short Answer

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

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

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Given information

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

Step 2. Solve the integration by parts .

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

$u = x d u = d x$

and

$d v = \frac{d x}{e^{x}} v = \int \frac{d x}{e^{x}} v = - \frac{1}{e^{x}}$

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

$\int \frac{x}{e^{x}} d x = (x (- \frac{1}{e^{x}}) - \int (- \frac{1}{e^{x}}) d x) = (- \frac{x}{e^{x}}) + \int e^{- x} d x$

Step 3. Integration by parts.

We have, $u = - x d u = - d x$

So,

$(- \frac{x}{e^{x}}) + \int e^{- x} d u = (- \frac{x}{e^{x}}) - e^{- x} + c = - x e^{x} - e^{x} + c$

Find Study Materials for

Create Study Materials

Select your language

Calculus

Answers without the blur.

Short Answer

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

Step by Step Solution

Step 1. Given information

Step 2. Solve the integration by parts .

Step 3. Integration by parts.

Most popular questions for Math Textbooks

Want to see more solutions like these?

Recommended explanations on Math Textbooks

Select your language

Calculus

Answers without the blur.

Short Answer

Solve the integral: ∫xexdx

Step by Step Solution

Step 1. Given information

Step 2. Solve the integration by parts .

Step 3. Integration by parts.

Most popular questions for Math Textbooks

Want to see more solutions like these?

Recommended explanations on Math Textbooks

Decision Maths

Calculus

Probability and Statistics

Statistics

Mechanics Maths

Geometry

Pure Maths

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