3.48 \(\int (8+8 x-x^3+8 x^4) \, dx\)

Optimal. Leaf size=23 \[ \frac{8 x^5}{5}-\frac{x^4}{4}+4 x^2+8 x \]

[Out]

8*x + 4*x^2 - x^4/4 + (8*x^5)/5

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Rubi [A]  time = 0.0030522, antiderivative size = 23, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 0, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0., Rules used = {} \[ \frac{8 x^5}{5}-\frac{x^4}{4}+4 x^2+8 x \]

Antiderivative was successfully verified.

[In]

Int[8 + 8*x - x^3 + 8*x^4,x]

[Out]

8*x + 4*x^2 - x^4/4 + (8*x^5)/5

Rubi steps

\begin{align*} \int \left (8+8 x-x^3+8 x^4\right ) \, dx &=8 x+4 x^2-\frac{x^4}{4}+\frac{8 x^5}{5}\\ \end{align*}

Mathematica [A]  time = 0.0000439, size = 23, normalized size = 1. \[ \frac{8 x^5}{5}-\frac{x^4}{4}+4 x^2+8 x \]

Antiderivative was successfully verified.

[In]

Integrate[8 + 8*x - x^3 + 8*x^4,x]

[Out]

8*x + 4*x^2 - x^4/4 + (8*x^5)/5

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Maple [A]  time = 0.001, size = 20, normalized size = 0.9 \begin{align*} 8\,x+4\,{x}^{2}-{\frac{{x}^{4}}{4}}+{\frac{8\,{x}^{5}}{5}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(8*x^4-x^3+8*x+8,x)

[Out]

8*x+4*x^2-1/4*x^4+8/5*x^5

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Maxima [A]  time = 1.16148, size = 26, normalized size = 1.13 \begin{align*} \frac{8}{5} \, x^{5} - \frac{1}{4} \, x^{4} + 4 \, x^{2} + 8 \, x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(8*x^4-x^3+8*x+8,x, algorithm="maxima")

[Out]

8/5*x^5 - 1/4*x^4 + 4*x^2 + 8*x

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Fricas [A]  time = 1.08171, size = 45, normalized size = 1.96 \begin{align*} \frac{8}{5} x^{5} - \frac{1}{4} x^{4} + 4 x^{2} + 8 x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(8*x^4-x^3+8*x+8,x, algorithm="fricas")

[Out]

8/5*x^5 - 1/4*x^4 + 4*x^2 + 8*x

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Sympy [A]  time = 0.053158, size = 19, normalized size = 0.83 \begin{align*} \frac{8 x^{5}}{5} - \frac{x^{4}}{4} + 4 x^{2} + 8 x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(8*x**4-x**3+8*x+8,x)

[Out]

8*x**5/5 - x**4/4 + 4*x**2 + 8*x

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Giac [A]  time = 1.12515, size = 26, normalized size = 1.13 \begin{align*} \frac{8}{5} \, x^{5} - \frac{1}{4} \, x^{4} + 4 \, x^{2} + 8 \, x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(8*x^4-x^3+8*x+8,x, algorithm="giac")

[Out]

8/5*x^5 - 1/4*x^4 + 4*x^2 + 8*x