What is the integral of 5-3x^3+2x^2 ?

The integral of 5-3x^3+2x^2 is 5x-(3x^4)/4+(2x^3)/3+C

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integral of 5-3x^3+2x^2

\int 5 - 3 x^{3} + 2 x^{2} d x

5 x - \frac{3 x ^{4}}{4} + \frac{2 x ^{3}}{3} + C

Solution steps

\int 5 - 3 x^{3} + 2 x^{2} 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 3 x^{3} d x + \int 2 x^{2} d x

\int 5 d x = 5 x

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

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

= 5 x - \frac{3 x ^{4}}{4} + \frac{2 x ^{3}}{3}

Add a constant to the solution

= 5 x - \frac{3 x ^{4}}{4} + \frac{2 x ^{3}}{3} + C

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What is the integral of 5-3x^3+2x^2 ?
The integral of 5-3x^3+2x^2 is 5x-(3x^4)/4+(2x^3)/3+C