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Q 28.

Expert-verified

Calculus

Found in: Page 429

Book edition 1st

Author(s) Peter Kohn, Laura Taalman

Pages 1155 pages

ISBN 9781429241861

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Short Answer

Solve the integral: $\int x \sin x d x$

The required answer is $- x \cos x + \sin x + c$ .

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 $\int x \sin x d x$ .

Step 2. Solve the integration by parts .

We have,

$u = x d u = d x$

and

localid="1648636397500" $d v = \sin x d x v = \int \sin x d x v = - \cos x$

The formula of integration by parts is localid="1648645366461" $\int u d v = u v - \int v d u$

$\int x \sin x d x = x (- \cos x) - \int (- \cos x) d x = - x \cos x + \int \cos x = - x \cos x + \sin x + c$

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