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

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

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

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

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

Solution steps

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

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

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

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

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

Add a constant to the solution

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

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