What is the integral of xsin(x/5) ?

The integral of xsin(x/5) is -5xcos(x/5)+25sin(x/5)+C

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integral of xsin(x/5)

\int x sin (\frac{x}{5}) d x

- 5 x cos (\frac{x}{5}) + 25 sin (\frac{x}{5}) + C

Solution steps

\int x sin (\frac{x}{5}) d x

Apply Integration By Parts

: - 5 x cos (\frac{x}{5}) - \int - 5 cos (\frac{x}{5}) d x

= - 5 x cos (\frac{x}{5}) - \int - 5 cos (\frac{x}{5}) d x

\int - 5 cos (\frac{x}{5}) d x = - 25 sin (\frac{x}{5})

= - 5 x cos (\frac{x}{5}) - (- 25 sin (\frac{x}{5}))

Simplify

= - 5 x cos (\frac{x}{5}) + 25 sin (\frac{x}{5})

Add a constant to the solution

= - 5 x cos (\frac{x}{5}) + 25 sin (\frac{x}{5}) + C

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What is the integral of xsin(x/5) ?
The integral of xsin(x/5) is -5xcos(x/5)+25sin(x/5)+C