What is the integral of x^4+x^3-6x^2 ?

The integral of x^4+x^3-6x^2 is (x^5)/5+(x^4)/4-2x^3+C

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integral of x^4+x^3-6x^2

\int x^{4} + x^{3} - 6 x^{2} d x

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

Solution steps

\int x^{4} + x^{3} - 6 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^{4} d x + \int x^{3} d x - \int 6 x^{2} d x

\int x^{4} d x = \frac{x ^{5}}{5}

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

\int 6 x^{2} d x = 2 x^{3}

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

Add a constant to the solution

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

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What is the integral of x^4+x^3-6x^2 ?
The integral of x^4+x^3-6x^2 is (x^5)/5+(x^4)/4-2x^3+C