ringearV

## Answered question

2021-09-25

Solve the following indefinite integrals.
$\int \mathrm{sin}\frac{x}{2}\mathrm{cos}\frac{x}{2}dx$

### Answer & Explanation

l1koV

Skilled2021-09-26Added 100 answers

To find:
The indefinite integral of $\int \mathrm{sin}\left(\frac{x}{2}\right)\mathrm{cos}\left(\frac{x}{2}\right)dx$
Calculation:
The indefinite integral of $\int \mathrm{sin}\left(\frac{x}{2}\right)\mathrm{cos}\left(\frac{x}{2}\right)dx$ can be obtained as,
$\int \mathrm{sin}\left(\frac{x}{2}\right)\mathrm{cos}\left(\frac{x}{2}\right)dx=\frac{1}{2}\int 2\mathrm{sin}\left(\frac{x}{2}\right)\mathrm{cos}\left(\frac{x}{2}\right)dx$
$=\frac{1}{2}\int \mathrm{sin}xdx$
$=-\frac{1}{2}\mathrm{cos}x+C$
Thus, the integral of

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