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Expert-verified Found in: Page 429 ### Calculus

Book edition 1st
Author(s) Peter Kohn, Laura Taalman
Pages 1155 pages
ISBN 9781429241861 # Solve the integral: $\int x\mathrm{sin}xdx$

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

See the step by step solution

## Step 1. Given information.

We have given integral is $\int x\mathrm{sin}xdx$.

## Step 2. Solve the integration by parts .

We have,

$u=x\phantom{\rule{0ex}{0ex}}du=dx$

and

localid="1648636397500" $dv=\mathrm{sin}xdx\phantom{\rule{0ex}{0ex}}v=\int \mathrm{sin}xdx\phantom{\rule{0ex}{0ex}}v=-\mathrm{cos}x$

The formula of integration by parts is localid="1648645366461" $\int udv=uv-\int vdu$

$\int x\mathrm{sin}xdx\phantom{\rule{0ex}{0ex}}=x\left(-\mathrm{cos}x\right)-\int \left(-\mathrm{cos}x\right)dx\phantom{\rule{0ex}{0ex}}=-x\mathrm{cos}x+\int \mathrm{cos}x\phantom{\rule{0ex}{0ex}}=-x\mathrm{cos}x+\mathrm{sin}x+c$ ### Want to see more solutions like these? 