What is the integral of x^3-pix^2 ?

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

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integral of x^3-pix^2

\int x^{3} - π x^{2} d x

\frac{x ^{4}}{4} - \frac{π x ^{3}}{3} + C

Solution steps

\int x^{3} - π 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 x^{3} d x - \int π x^{2} d x

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

\int π x^{2} d x = \frac{π x ^{3}}{3}

= \frac{x ^{4}}{4} - \frac{π x ^{3}}{3}

Add a constant to the solution

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

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