What is the integral of xcos(x/3) ?

The integral of xcos(x/3) is 3xsin(x/3)+9cos(x/3)+C

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integral of xcos(x/3)

\int x cos (\frac{x}{3}) d x

3 x sin (\frac{x}{3}) + 9 cos (\frac{x}{3}) + C

Solution steps

\int x cos (\frac{x}{3}) d x

Apply Integration By Parts

: 3 x sin (\frac{x}{3}) - \int 3 sin (\frac{x}{3}) d x

= 3 x sin (\frac{x}{3}) - \int 3 sin (\frac{x}{3}) d x

\int 3 sin (\frac{x}{3}) d x = - 9 cos (\frac{x}{3})

= 3 x sin (\frac{x}{3}) - (- 9 cos (\frac{x}{3}))

Simplify

= 3 x sin (\frac{x}{3}) + 9 cos (\frac{x}{3})

Add a constant to the solution

= 3 x sin (\frac{x}{3}) + 9 cos (\frac{x}{3}) + C

\int cos (x) csc^{6} (x) d x

\int \frac{1}{3 + y} d y

\int_{0}^{1} \frac{1}{1 + 9 x ^{2}} d x

\frac{\partial}{\partial x} (2 x - 4)

\frac{\partial}{\partial y} (- sin (x y))

What is the integral of xcos(x/3) ?
The integral of xcos(x/3) is 3xsin(x/3)+9cos(x/3)+C