What is the integral of (-x+4sin(x)) ?

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

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integral of (-x+4sin(x))

\int (- x + 4 sin (x)) d x

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

Solution steps

\int - x + 4 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 x d x + \int 4 sin (x) d x

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

\int 4 sin (x) d x = - 4 cos (x)

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

Add a constant to the solution

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

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