3.87.97 \(\int (2 x-16 x^3+24 x^5+e^9 (-2+12 x^2)+(2-12 x^2) \log (2)) \, dx\)

Optimal. Leaf size=20 \[ e^3+\left (-e^9+x-2 x^3+\log (2)\right )^2 \]

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Rubi [A]  time = 0.01, antiderivative size = 40, normalized size of antiderivative = 2.00, number of steps used = 3, number of rules used = 0, integrand size = 35, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} 4 x^6-4 x^4+4 e^9 x^3-4 x^3 \log (2)+x^2-2 e^9 x+2 x \log (2) \end {gather*}

Antiderivative was successfully verified.

[In]

Int[2*x - 16*x^3 + 24*x^5 + E^9*(-2 + 12*x^2) + (2 - 12*x^2)*Log[2],x]

[Out]

-2*E^9*x + x^2 + 4*E^9*x^3 - 4*x^4 + 4*x^6 + 2*x*Log[2] - 4*x^3*Log[2]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=x^2-4 x^4+4 x^6+e^9 \int \left (-2+12 x^2\right ) \, dx+\log (2) \int \left (2-12 x^2\right ) \, dx\\ &=-2 e^9 x+x^2+4 e^9 x^3-4 x^4+4 x^6+2 x \log (2)-4 x^3 \log (2)\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.01, size = 27, normalized size = 1.35 \begin {gather*} x \left (-1+2 x^2\right ) \left (2 e^9-x+2 x^3-\log (4)\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[2*x - 16*x^3 + 24*x^5 + E^9*(-2 + 12*x^2) + (2 - 12*x^2)*Log[2],x]

[Out]

x*(-1 + 2*x^2)*(2*E^9 - x + 2*x^3 - Log[4])

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fricas [A]  time = 0.50, size = 40, normalized size = 2.00 \begin {gather*} 4 \, x^{6} - 4 \, x^{4} + x^{2} + 2 \, {\left (2 \, x^{3} - x\right )} e^{9} - 2 \, {\left (2 \, x^{3} - x\right )} \log \relax (2) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-12*x^2+2)*log(2)+(12*x^2-2)*exp(9)+24*x^5-16*x^3+2*x,x, algorithm="fricas")

[Out]

4*x^6 - 4*x^4 + x^2 + 2*(2*x^3 - x)*e^9 - 2*(2*x^3 - x)*log(2)

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giac [A]  time = 0.13, size = 40, normalized size = 2.00 \begin {gather*} 4 \, x^{6} - 4 \, x^{4} + x^{2} + 2 \, {\left (2 \, x^{3} - x\right )} e^{9} - 2 \, {\left (2 \, x^{3} - x\right )} \log \relax (2) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-12*x^2+2)*log(2)+(12*x^2-2)*exp(9)+24*x^5-16*x^3+2*x,x, algorithm="giac")

[Out]

4*x^6 - 4*x^4 + x^2 + 2*(2*x^3 - x)*e^9 - 2*(2*x^3 - x)*log(2)

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maple [B]  time = 0.03, size = 39, normalized size = 1.95

method	result	size
default	\(\ln \relax (2) \left (-4 x^{3}+2 x \right )+{\mathrm e}^{9} \left (4 x^{3}-2 x \right )+4 x^{6}-4 x^{4}+x^{2}\)	\(39\)
norman	\(x^{2}+\left (-4 \ln \relax (2)+4 \,{\mathrm e}^{9}\right ) x^{3}+\left (2 \ln \relax (2)-2 \,{\mathrm e}^{9}\right ) x -4 x^{4}+4 x^{6}\)	\(39\)
risch	\(-4 x^{3} \ln \relax (2)+2 x \ln \relax (2)+4 x^{3} {\mathrm e}^{9}-2 x \,{\mathrm e}^{9}+4 x^{6}-4 x^{4}+x^{2}\)	\(39\)
gosper	\(-x \left (-4 x^{5}+4 x^{2} \ln \relax (2)-4 x^{2} {\mathrm e}^{9}+4 x^{3}-2 \ln \relax (2)+2 \,{\mathrm e}^{9}-x \right )\)	\(40\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((-12*x^2+2)*ln(2)+(12*x^2-2)*exp(9)+24*x^5-16*x^3+2*x,x,method=_RETURNVERBOSE)

[Out]

ln(2)*(-4*x^3+2*x)+exp(9)*(4*x^3-2*x)+4*x^6-4*x^4+x^2

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maxima [A]  time = 0.36, size = 40, normalized size = 2.00 \begin {gather*} 4 \, x^{6} - 4 \, x^{4} + x^{2} + 2 \, {\left (2 \, x^{3} - x\right )} e^{9} - 2 \, {\left (2 \, x^{3} - x\right )} \log \relax (2) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-12*x^2+2)*log(2)+(12*x^2-2)*exp(9)+24*x^5-16*x^3+2*x,x, algorithm="maxima")

[Out]

4*x^6 - 4*x^4 + x^2 + 2*(2*x^3 - x)*e^9 - 2*(2*x^3 - x)*log(2)

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mupad [B]  time = 0.05, size = 39, normalized size = 1.95 \begin {gather*} 4\,x^6-4\,x^4+\left (4\,{\mathrm {e}}^9-4\,\ln \relax (2)\right )\,x^3+x^2+\left (\ln \relax (4)-2\,{\mathrm {e}}^9\right )\,x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(2*x + exp(9)*(12*x^2 - 2) - log(2)*(12*x^2 - 2) - 16*x^3 + 24*x^5,x)

[Out]

x^3*(4*exp(9) - 4*log(2)) - x*(2*exp(9) - log(4)) + x^2 - 4*x^4 + 4*x^6

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sympy [B]  time = 0.06, size = 37, normalized size = 1.85 \begin {gather*} 4 x^{6} - 4 x^{4} + x^{3} \left (- 4 \log {\relax (2 )} + 4 e^{9}\right ) + x^{2} + x \left (- 2 e^{9} + 2 \log {\relax (2 )}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-12*x**2+2)*ln(2)+(12*x**2-2)*exp(9)+24*x**5-16*x**3+2*x,x)

[Out]

4*x**6 - 4*x**4 + x**3*(-4*log(2) + 4*exp(9)) + x**2 + x*(-2*exp(9) + 2*log(2))

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