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

The integral of sin(x)-x^4 is -cos(x)-(x^5)/5+C

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integral of sin(x)-x^4

\int sin (x) - x^{4} d x

- cos (x) - \frac{x ^{5}}{5} + C

Solution steps

\int sin (x) - x^{4} 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 x^{4} d x

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

\int x^{4} d x = \frac{x ^{5}}{5}

= - cos (x) - \frac{x ^{5}}{5}

Add a constant to the solution

= - cos (x) - \frac{x ^{5}}{5} + C

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What is the integral of sin(x)-x^4 ?
The integral of sin(x)-x^4 is -cos(x)-(x^5)/5+C