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

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

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integral of x^2cos((nx)/2)

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

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

Solution steps

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

Apply Integration By Parts

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

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

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

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

Add a constant to the solution

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

\int 5 + 4 x^{2} d x

ln (2^{x} - 4)

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

y = (25 - 4 x^{2})^{2}, x = - \frac{5}{2}, x = \frac{5}{2}

\int \frac{5 x + 3}{x ^{2} + 1} d x

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