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

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Rubi [A]  time = 0.00, antiderivative size = 23, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 0, integrand size = 15, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, 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*}

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Mathematica [A]  time = 0.00, size = 23, normalized size = 1.00 \[ \frac {8 x^5}{5}-\frac {x^4}{4}+4 x^2+8 x \]

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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fricas [A]  time = 0.35, size = 19, normalized size = 0.83 \[ \frac {8}{5} x^{5} - \frac {1}{4} x^{4} + 4 x^{2} + 8 x \]

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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giac [A]  time = 0.32, size = 19, normalized size = 0.83 \[ \frac {8}{5} \, x^{5} - \frac {1}{4} \, x^{4} + 4 \, x^{2} + 8 \, x \]

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

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maple [A]  time = 0.00, size = 20, normalized size = 0.87 \[ \frac {8}{5} x^{5}-\frac {1}{4} x^{4}+4 x^{2}+8 x \]

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 = 0.91, size = 19, normalized size = 0.83 \[ \frac {8}{5} \, x^{5} - \frac {1}{4} \, x^{4} + 4 \, x^{2} + 8 \, x \]

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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mupad [B]  time = 0.03, size = 19, normalized size = 0.83 \[ \frac {8\,x^5}{5}-\frac {x^4}{4}+4\,x^2+8\,x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(8*x - x^3 + 8*x^4 + 8,x)

[Out]

8*x + 4*x^2 - x^4/4 + (8*x^5)/5

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sympy [A]  time = 0.06, size = 19, normalized size = 0.83 \[ \frac {8 x^{5}}{5} - \frac {x^{4}}{4} + 4 x^{2} + 8 x \]

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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