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

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

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integral of (x^2-x)cos(x)

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

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

Solution steps

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

Expand

(x^{2} - x) cos (x) : x^{2} cos (x) - x cos (x)

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

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

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

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

\int x cos (x) d x = x sin (x) + cos (x)

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

Simplify

x^{2} sin (x) - 2 (- x cos (x) + sin (x)) - (x sin (x) + cos (x)) : x^{2} sin (x) + 2 x cos (x) - 2 sin (x) - x sin (x) - cos (x)

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

Add a constant to the solution

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

x \to 5 - lim (\frac{2}{( x - 5 )})

3 x^{2} e^{x} + e^{x} (x^{3} + 5)

y e^{2 x} d x - (4 + e^{2 x}) d y = 0

\int_{0}^{2 π} cos^{4} (x) d x

\int_{0}^{\frac{π}{20}} cos (10 x) d x

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