What is the integral of xsin(x/2) ?

The integral of xsin(x/2) is -2xcos(x/2)+4sin(x/2)+C

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integral of xsin(x/2)

\int x sin (\frac{x}{2}) d x

- 2 x cos (\frac{x}{2}) + 4 sin (\frac{x}{2}) + C

Solution steps

\int x sin (\frac{x}{2}) d x

Apply Integration By Parts

: - 2 x cos (\frac{x}{2}) - \int - 2 cos (\frac{x}{2}) d x

= - 2 x cos (\frac{x}{2}) - \int - 2 cos (\frac{x}{2}) d x

\int - 2 cos (\frac{x}{2}) d x = - 4 sin (\frac{x}{2})

= - 2 x cos (\frac{x}{2}) - (- 4 sin (\frac{x}{2}))

Simplify

= - 2 x cos (\frac{x}{2}) + 4 sin (\frac{x}{2})

Add a constant to the solution

= - 2 x cos (\frac{x}{2}) + 4 sin (\frac{x}{2}) + C

f (t) = 4 t^{2} + 5

3 - \frac{x ^{2}}{2}, 1, 2

y^{^{'}} + 20 y = 40 sin (60 x)

\frac{\partial}{\partial x} (sin (8 x) cos (3 y))

y = x^{2}, y = 4 x

What is the integral of xsin(x/2) ?
The integral of xsin(x/2) is -2xcos(x/2)+4sin(x/2)+C