What is the integral of x^2-3x^3-10x-1 ?

The integral of x^2-3x^3-10x-1 is (x^3)/3-(3x^4)/4-5x^2-x+C

integral of x^2-3x^3-10x-1

\int x^{2} - 3 x^{3} - 10 x - 1 d x

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

Solution steps

\int x^{2} - 3 x^{3} - 10 x - 1 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^{2} d x - \int 3 x^{3} d x - \int 10 x d x - \int 1 d x

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

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

\int 10 x d x = 5 x^{2}

\int 1 d x = x

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

Add a constant to the solution

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

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What is the integral of x^2-3x^3-10x-1 ?
The integral of x^2-3x^3-10x-1 is (x^3)/3-(3x^4)/4-5x^2-x+C