What is the integral of xcos(x/4) ?

The integral of xcos(x/4) is 4xsin(x/4)+16cos(x/4)+C

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integral of xcos(x/4)

\int x cos (\frac{x}{4}) d x

4 x sin (\frac{x}{4}) + 16 cos (\frac{x}{4}) + C

Solution steps

\int x cos (\frac{x}{4}) d x

Apply Integration By Parts

: 4 x sin (\frac{x}{4}) - \int 4 sin (\frac{x}{4}) d x

= 4 x sin (\frac{x}{4}) - \int 4 sin (\frac{x}{4}) d x

\int 4 sin (\frac{x}{4}) d x = - 16 cos (\frac{x}{4})

= 4 x sin (\frac{x}{4}) - (- 16 cos (\frac{x}{4}))

Simplify

= 4 x sin (\frac{x}{4}) + 16 cos (\frac{x}{4})

Add a constant to the solution

= 4 x sin (\frac{x}{4}) + 16 cos (\frac{x}{4}) + C

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What is the integral of xcos(x/4) ?
The integral of xcos(x/4) is 4xsin(x/4)+16cos(x/4)+C