What is the integral of (RAyx-3/2 x^2+5) ?

The integral of (RAyx-3/2 x^2+5) is 5x-(x^3)/2+(ARyx^2)/2+C

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integral of (RAyx-3/2 x^2+5)

\int (R A y x - \frac{3}{2} x^{2} + 5) d x

5 x - \frac{x ^{3}}{2} + \frac{A R y x ^{2}}{2} + C

Solution steps

\int R A y x - \frac{3}{2} x^{2} + 5 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 5 d x - \int \frac{3}{2} x^{2} d x + \int A R y x d x

\int 5 d x = 5 x

\int \frac{3}{2} x^{2} d x = \frac{x ^{3}}{2}

\int A R y x d x = \frac{A R y x ^{2}}{2}

= 5 x - \frac{x ^{3}}{2} + \frac{A R y x ^{2}}{2}

Add a constant to the solution

= 5 x - \frac{x ^{3}}{2} + \frac{A R y x ^{2}}{2} + C

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What is the integral of (RAyx-3/2 x^2+5) ?
The integral of (RAyx-3/2 x^2+5) is 5x-(x^3)/2+(ARyx^2)/2+C