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

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

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integral of (x-sin(x))

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

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

Solution steps

\int x - 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 sin (x) d x

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

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

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

Simplify

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

Add a constant to the solution

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

\int (x^{2} + 9 x) cos (x) d x

f (x) = (3 x - 2)^{2} (5 x + 4)

x \to \infty + lim (\frac{x ^{3}}{1 e ^{\frac{x}{4}}})

\frac{\partial}{\partial x} (x^{ey})

\int \frac{1}{x ^{2} + 3 x + 4} d x

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