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

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

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integral of xcos(x/5)

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

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

Solution steps

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

Apply Integration By Parts

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

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

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

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

Simplify

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

Add a constant to the solution

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

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