What is the integral of yt^3-1.5y ?

The integral of yt^3-1.5y is -1.5yt+0.25yt^4+C

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integral of yt^3-1.5y

\int y t^{3} - 1.5 y d t

- 1.5 y t + 0.25 y t^{4} + C

Solution steps

\int y t^{3} - 1.5 y d t

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= - \int 1.5 y d t + \int y t^{3} d t

\int 1.5 y d t = 1.5 y t

\int y t^{3} d t = \frac{y t ^{4}}{4}

= - 1.5 y t + \frac{y t ^{4}}{4}

Simplify

= - 1.5 y t + 0.25 y t^{4}

Add a constant to the solution

= - 1.5 y t + 0.25 y t^{4} + C

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What is the integral of yt^3-1.5y ?
The integral of yt^3-1.5y is -1.5yt+0.25yt^4+C