What is the integral of 2-1(x^3+5x^2-1) ?

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

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integral of 2-1(x^3+5x^2-1)

\int 2 - 1 (x^{3} + 5 x^{2} - 1) d x

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

Solution steps

\int 2 - 1 \cdot (x^{3} + 5 x^{2} - 1) d x

Simplify

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

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

\int 5 x^{2} d x = \frac{5 x ^{3}}{3}

\int 3 d x = 3 x

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

Add a constant to the solution

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

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