3.119 \(\int (a+8 x-8 x^2+4 x^3-x^4) \, dx\)

Optimal. Leaf size=26 \[ a x-\frac {x^5}{5}+x^4-\frac {8 x^3}{3}+4 x^2 \]

[Out]

a*x+4*x^2-8/3*x^3+x^4-1/5*x^5

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Rubi [A]  time = 0.00, antiderivative size = 26, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 0, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \[ a x-\frac {x^5}{5}+x^4-\frac {8 x^3}{3}+4 x^2 \]

Antiderivative was successfully verified.

[In]

Int[a + 8*x - 8*x^2 + 4*x^3 - x^4,x]

[Out]

a*x + 4*x^2 - (8*x^3)/3 + x^4 - x^5/5

Rubi steps

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

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Mathematica [A]  time = 0.00, size = 26, normalized size = 1.00 \[ a x-\frac {x^5}{5}+x^4-\frac {8 x^3}{3}+4 x^2 \]

Antiderivative was successfully verified.

[In]

Integrate[a + 8*x - 8*x^2 + 4*x^3 - x^4,x]

[Out]

a*x + 4*x^2 - (8*x^3)/3 + x^4 - x^5/5

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fricas [A]  time = 0.35, size = 22, normalized size = 0.85 \[ -\frac {1}{5} x^{5} + x^{4} - \frac {8}{3} x^{3} + 4 x^{2} + x a \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-x^4+4*x^3-8*x^2+a+8*x,x, algorithm="fricas")

[Out]

-1/5*x^5 + x^4 - 8/3*x^3 + 4*x^2 + x*a

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giac [A]  time = 0.30, size = 22, normalized size = 0.85 \[ -\frac {1}{5} \, x^{5} + x^{4} - \frac {8}{3} \, x^{3} + a x + 4 \, x^{2} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-x^4+4*x^3-8*x^2+a+8*x,x, algorithm="giac")

[Out]

-1/5*x^5 + x^4 - 8/3*x^3 + a*x + 4*x^2

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maple [A]  time = 0.00, size = 23, normalized size = 0.88 \[ -\frac {1}{5} x^{5}+x^{4}-\frac {8}{3} x^{3}+a x +4 x^{2} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-x^4+4*x^3-8*x^2+a+8*x,x)

[Out]

a*x+4*x^2-8/3*x^3+x^4-1/5*x^5

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maxima [A]  time = 0.63, size = 22, normalized size = 0.85 \[ -\frac {1}{5} \, x^{5} + x^{4} - \frac {8}{3} \, x^{3} + a x + 4 \, x^{2} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-x^4+4*x^3-8*x^2+a+8*x,x, algorithm="maxima")

[Out]

-1/5*x^5 + x^4 - 8/3*x^3 + a*x + 4*x^2

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mupad [B]  time = 0.02, size = 22, normalized size = 0.85 \[ -\frac {x^5}{5}+x^4-\frac {8\,x^3}{3}+4\,x^2+a\,x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(a + 8*x - 8*x^2 + 4*x^3 - x^4,x)

[Out]

a*x + 4*x^2 - (8*x^3)/3 + x^4 - x^5/5

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sympy [A]  time = 0.06, size = 22, normalized size = 0.85 \[ a x - \frac {x^{5}}{5} + x^{4} - \frac {8 x^{3}}{3} + 4 x^{2} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-x**4+4*x**3-8*x**2+a+8*x,x)

[Out]

a*x - x**5/5 + x**4 - 8*x**3/3 + 4*x**2

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