What is the integral of x*sin(x/2) ?

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

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integral of x*sin(x/2)

\int x \cdot 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

0.72 x^{3} - 4.8 x^{2} + 0.6 x + 7.6

\int_{- 1}^{1} e^{x} - (x^{2} - 2) d x

\frac{\partial}{\partial x} (\frac{2 x - y}{x + 2 y})

\frac{\partial ^{2}}{\partial x ^{2}} (x^{2} - y^{2})

\frac{\partial}{\partial x} ((4 - x^{2} - y^{2})^{\frac{1}{2}})

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