3.57.85 \(\int (-2 x+18 x^2+8 x^3) \, dx\)

Optimal. Leaf size=20 \[ 3-e^e-x^2+2 x^3 (3+x) \]

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Rubi [A]  time = 0.00, antiderivative size = 16, normalized size of antiderivative = 0.80, number of steps used = 1, number of rules used = 0, integrand size = 14, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} 2 x^4+6 x^3-x^2 \end {gather*}

Antiderivative was successfully verified.

[In]

Int[-2*x + 18*x^2 + 8*x^3,x]

[Out]

-x^2 + 6*x^3 + 2*x^4

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=-x^2+6 x^3+2 x^4\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 16, normalized size = 0.80 \begin {gather*} -x^2+6 x^3+2 x^4 \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[-2*x + 18*x^2 + 8*x^3,x]

[Out]

-x^2 + 6*x^3 + 2*x^4

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fricas [A]  time = 0.50, size = 16, normalized size = 0.80 \begin {gather*} 2 \, x^{4} + 6 \, x^{3} - x^{2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(8*x^3+18*x^2-2*x,x, algorithm="fricas")

[Out]

2*x^4 + 6*x^3 - x^2

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giac [A]  time = 0.18, size = 16, normalized size = 0.80 \begin {gather*} 2 \, x^{4} + 6 \, x^{3} - x^{2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(8*x^3+18*x^2-2*x,x, algorithm="giac")

[Out]

2*x^4 + 6*x^3 - x^2

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maple [A]  time = 0.02, size = 15, normalized size = 0.75

method	result	size
gosper	\(x^{2} \left (2 x^{2}+6 x -1\right )\)	\(15\)
default	\(2 x^{4}+6 x^{3}-x^{2}\)	\(17\)
norman	\(2 x^{4}+6 x^{3}-x^{2}\)	\(17\)
risch	\(2 x^{4}+6 x^{3}-x^{2}\)	\(17\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(8*x^3+18*x^2-2*x,x,method=_RETURNVERBOSE)

[Out]

x^2*(2*x^2+6*x-1)

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maxima [A]  time = 0.35, size = 16, normalized size = 0.80 \begin {gather*} 2 \, x^{4} + 6 \, x^{3} - x^{2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(8*x^3+18*x^2-2*x,x, algorithm="maxima")

[Out]

2*x^4 + 6*x^3 - x^2

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mupad [B]  time = 0.03, size = 14, normalized size = 0.70 \begin {gather*} x^2\,\left (2\,x^2+6\,x-1\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(18*x^2 - 2*x + 8*x^3,x)

[Out]

x^2*(6*x + 2*x^2 - 1)

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sympy [A]  time = 0.05, size = 12, normalized size = 0.60 \begin {gather*} 2 x^{4} + 6 x^{3} - x^{2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(8*x**3+18*x**2-2*x,x)

[Out]

2*x**4 + 6*x**3 - x**2

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