What is the integral of x^2cos(x/2) ?

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

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integral of x^2cos(x/2)

\int x^{2} cos (\frac{x}{2}) d x

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

Solution steps

\int x^{2} cos (\frac{x}{2}) d x

Apply Integration By Parts

: 2 x^{2} sin (\frac{x}{2}) - \int 4 x sin (\frac{x}{2}) d x

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

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

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

Add a constant to the solution

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

e^{t}

\int \frac{t ^{2}}{1 - t ^{6}} d t

\int e^{t^{2}} t^{3} d t

\frac{d ^{2}}{d x ^{2}} (4 x^{3} - 5 x^{4})

sin (x y) = cos (x + y)

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