What is the integral of sin(0.01x)+x^3 ?

The integral of sin(0.01x)+x^3 is -100cos(0.01x)+0.25x^4+C

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integral of sin(0.01x)+x^3

\int sin (0.01 x) + x^{3} d x

- 100 cos (0.01 x) + 0.25 x^{4} + C

Solution steps

\int sin (0.01 x) + x^{3} 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 (0.01 x) d x + \int x^{3} d x

\int sin (0.01 x) d x = - 100 cos (0.01 x)

\int x^{3} d x = \frac{x ^{4}}{4}

= - 100 cos (0.01 x) + \frac{x ^{4}}{4}

Simplify

= - 100 cos (0.01 x) + 0.25 x^{4}

Add a constant to the solution

= - 100 cos (0.01 x) + 0.25 x^{4} + C

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What is the integral of sin(0.01x)+x^3 ?
The integral of sin(0.01x)+x^3 is -100cos(0.01x)+0.25x^4+C