3.76.24 \(\int (-1-20 e^2+9 x^8) \, dx\)

Optimal. Leaf size=12 \[ x \left (-1-20 e^2+x^8\right ) \]

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Rubi [A]  time = 0.00, antiderivative size = 14, normalized size of antiderivative = 1.17, number of steps used = 1, number of rules used = 0, integrand size = 12, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} x^9-\left (1+20 e^2\right ) x \end {gather*}

Antiderivative was successfully verified.

[In]

Int[-1 - 20*E^2 + 9*x^8,x]

[Out]

-((1 + 20*E^2)*x) + x^9

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=-\left (\left (1+20 e^2\right ) x\right )+x^9\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 13, normalized size = 1.08 \begin {gather*} -x-20 e^2 x+x^9 \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[-1 - 20*E^2 + 9*x^8,x]

[Out]

-x - 20*E^2*x + x^9

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fricas [A]  time = 0.88, size = 15, normalized size = 1.25 \begin {gather*} x^{9} - x e^{\left (\log \left (20\right ) + 2\right )} - x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-exp(log(20)+2)+9*x^8-1,x, algorithm="fricas")

[Out]

x^9 - x*e^(log(20) + 2) - x

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giac [A]  time = 0.14, size = 15, normalized size = 1.25 \begin {gather*} x^{9} - x e^{\left (\log \left (20\right ) + 2\right )} - x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-exp(log(20)+2)+9*x^8-1,x, algorithm="giac")

[Out]

x^9 - x*e^(log(20) + 2) - x

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maple [A]  time = 0.03, size = 13, normalized size = 1.08

method	result	size
norman	\(x^{9}+\left (-20 \,{\mathrm e}^{2}-1\right ) x\)	\(13\)
risch	\(-20 \,{\mathrm e}^{2} x +x^{9}-x\)	\(13\)
gosper	\(-x \left (-x^{8}+{\mathrm e}^{\ln \left (20\right )+2}+1\right )\)	\(16\)
default	\(-{\mathrm e}^{\ln \left (20\right )+2} x +x^{9}-x\)	\(16\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-exp(ln(20)+2)+9*x^8-1,x,method=_RETURNVERBOSE)

[Out]

x^9+(-20*exp(2)-1)*x

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maxima [A]  time = 0.37, size = 12, normalized size = 1.00 \begin {gather*} x^{9} - 20 \, x e^{2} - x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-exp(log(20)+2)+9*x^8-1,x, algorithm="maxima")

[Out]

x^9 - 20*x*e^2 - x

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mupad [B]  time = 5.54, size = 13, normalized size = 1.08 \begin {gather*} x^9-x\,\left (20\,{\mathrm {e}}^2+1\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(9*x^8 - exp(log(20) + 2) - 1,x)

[Out]

x^9 - x*(20*exp(2) + 1)

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sympy [A]  time = 0.05, size = 12, normalized size = 1.00 \begin {gather*} x^{9} + x \left (- 20 e^{2} - 1\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-exp(ln(20)+2)+9*x**8-1,x)

[Out]

x**9 + x*(-20*exp(2) - 1)

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