What is the integral of x(sin(x)-2) ?

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

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integral of x(sin(x)-2)

\int x (sin (x) - 2) d x

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

Solution steps

\int x (sin (x) - 2) d x

Expand

x (sin (x) - 2) : x sin (x) - 2 x

= \int x sin (x) - 2 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 sin (x) d x - \int 2 x d x

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

\int 2 x d x = x^{2}

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

Add a constant to the solution

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

\frac{\partial}{\partial x} (4^{(x^{9})})

\frac{d ^{2}}{d x ^{2}} (4 cos (x))

f (x) = \frac{4}{x ^{5}}

x \to - 2 lim (x^{2} + 5 x)

x \to 2 lim (3 x + 3)

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