What is the integral of x^2cos(1/5 x) ?

The integral of x^2cos(1/5 x) is 5x^2sin(1/5 x)-10(-5xcos(1/5 x)+25sin(1/5 x))+C

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integral of x^2cos(1/5 x)

\int x^{2} cos (\frac{1}{5} x) d x

5 x^{2} sin (\frac{1}{5} x) - 10 (- 5 x cos (\frac{1}{5} x) + 25 sin (\frac{1}{5} x)) + C

Solution steps

\int x^{2} cos (\frac{1}{5} x) d x

Apply Integration By Parts

: 5 x^{2} sin (\frac{1}{5} x) - \int 10 x sin (\frac{1}{5} x) d x

= 5 x^{2} sin (\frac{1}{5} x) - \int 10 x sin (\frac{1}{5} x) d x

\int 10 x sin (\frac{1}{5} x) d x = 10 (- 5 x cos (\frac{1}{5} x) + 25 sin (\frac{1}{5} x))

= 5 x^{2} sin (\frac{1}{5} x) - 10 (- 5 x cos (\frac{1}{5} x) + 25 sin (\frac{1}{5} x))

Add a constant to the solution

= 5 x^{2} sin (\frac{1}{5} x) - 10 (- 5 x cos (\frac{1}{5} x) + 25 sin (\frac{1}{5} x)) + C

f (x) = (4 - x) (\frac{2}{x ^{2}} - 3)

y = \frac{28}{x}

y = - e^{- x - 2}, (- 3, - e)

\frac{\partial}{\partial v} (v)

\frac{d}{d x} (x + y)

What is the integral of x^2cos(1/5 x) ?
The integral of x^2cos(1/5 x) is 5x^2sin(1/5 x)-10(-5xcos(1/5 x)+25sin(1/5 x))+C