What is the integral of x[2cos(x)-xsin(x)] ?

The integral of x[2cos(x)-xsin(x)] is x^2cos(x)+C

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integral of x[2cos(x)-xsin(x)]

\int x [2 cos (x) - x sin (x)] d x

x^{2} cos (x) + C

Solution steps

\int x [2 cos (x) - x sin (x)] d x

Expand

x [2 cos (x) - x sin (x)] : 2 x cos (x) - x^{2} sin (x)

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

\int 2 x cos (x) d x = 2 (x sin (x) + cos (x))

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

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

Simplify

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

= x^{2} cos (x)

Add a constant to the solution

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

x \to 2 lim (6 - 3 x - 3)

\int \frac{1}{1 + 9 x ^{2}} d x

\int \frac{8000 ln ( x + 25 )}{( x + 25 ) ^{2}} d x

\frac{\partial}{\partial y} (e^{- x yz})

\frac{d}{d x} (- x)

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