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

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

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

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

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

Solution steps

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

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

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

\int 1 d x = x

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

Add a constant to the solution

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

y^{^{'}} = (5 x + \frac{7}{x}) (7 x^{2} - 6)

(- 2.4) (9.4)

x \to 0 lim (\frac{1 - 1}{x})

\int \frac{7}{x ( x ^{2} + 1 )} d x

x \to 1 lim (\frac{2 x + 1}{1 - x})

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