3.56.5 \(\int e^{-\frac {4 (-3+\log (3))}{\log (2)}} (-e^{\frac {4 (-3+\log (3))}{\log (2)}}-4 x^3) \, dx\)

Optimal. Leaf size=23 \[ -x-e^{\frac {4 (3-\log (3))}{\log (2)}} x^4 \]

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Rubi [A]  time = 0.02, antiderivative size = 23, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 33, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.030, Rules used = {12} \begin {gather*} x^4 \left (-e^{\frac {4 (3-\log (3))}{\log (2)}}\right )-x \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(-E^((4*(-3 + Log[3]))/Log[2]) - 4*x^3)/E^((4*(-3 + Log[3]))/Log[2]),x]

[Out]

-x - E^((4*(3 - Log[3]))/Log[2])*x^4

Rule 12

Int[(a_)*(u_), x_Symbol] :> Dist[a, Int[u, x], x] /; FreeQ[a, x] &&  !MatchQ[u, (b_)*(v_) /; FreeQ[b, x]]

Rubi steps

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

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Mathematica [A]  time = 0.02, size = 25, normalized size = 1.09 \begin {gather*} -x-3^{-\frac {4}{\log (2)}} e^{\frac {12}{\log (2)}} x^4 \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-E^((4*(-3 + Log[3]))/Log[2]) - 4*x^3)/E^((4*(-3 + Log[3]))/Log[2]),x]

[Out]

-x - (E^(12/Log[2])*x^4)/3^(4/Log[2])

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fricas [A]  time = 1.05, size = 30, normalized size = 1.30 \begin {gather*} -{\left (x^{4} + x e^{\left (\frac {4 \, {\left (\log \relax (3) - 3\right )}}{\log \relax (2)}\right )}\right )} e^{\left (-\frac {4 \, {\left (\log \relax (3) - 3\right )}}{\log \relax (2)}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-exp((log(3)-3)/log(2))^4-4*x^3)/exp((log(3)-3)/log(2))^4,x, algorithm="fricas")

[Out]

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

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giac [A]  time = 0.17, size = 30, normalized size = 1.30 \begin {gather*} -{\left (x^{4} + x e^{\left (\frac {4 \, {\left (\log \relax (3) - 3\right )}}{\log \relax (2)}\right )}\right )} e^{\left (-\frac {4 \, {\left (\log \relax (3) - 3\right )}}{\log \relax (2)}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-exp((log(3)-3)/log(2))^4-4*x^3)/exp((log(3)-3)/log(2))^4,x, algorithm="giac")

[Out]

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

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maple [A]  time = 0.07, size = 25, normalized size = 1.09

method	result	size
risch	\(-3^{-\frac {4}{\ln \relax (2)}} x^{4} {\mathrm e}^{\frac {12}{\ln \relax (2)}}-x\)	\(25\)
gosper	\(-x \left ({\mathrm e}^{\frac {4 \ln \relax (3)-12}{\ln \relax (2)}}+x^{3}\right ) {\mathrm e}^{-\frac {4 \left (\ln \relax (3)-3\right )}{\ln \relax (2)}}\)	\(32\)
default	\({\mathrm e}^{-\frac {4 \left (\ln \relax (3)-3\right )}{\ln \relax (2)}} \left (-{\mathrm e}^{\frac {4 \ln \relax (3)-12}{\ln \relax (2)}} x -x^{4}\right )\)	\(35\)
norman	\(\left (-3^{-\frac {1}{\ln \relax (2)}} {\mathrm e}^{\frac {3}{\ln \relax (2)}} x^{4}-3^{\frac {3}{\ln \relax (2)}} {\mathrm e}^{-\frac {9}{\ln \relax (2)}} x \right ) {\mathrm e}^{-\frac {3 \left (\ln \relax (3)-3\right )}{\ln \relax (2)}}\)	\(53\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((-exp((ln(3)-3)/ln(2))^4-4*x^3)/exp((ln(3)-3)/ln(2))^4,x,method=_RETURNVERBOSE)

[Out]

-1/(3^(1/ln(2)))^4*x^4*exp(12/ln(2))-x

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maxima [A]  time = 0.37, size = 30, normalized size = 1.30 \begin {gather*} -{\left (x^{4} + x e^{\left (\frac {4 \, {\left (\log \relax (3) - 3\right )}}{\log \relax (2)}\right )}\right )} e^{\left (-\frac {4 \, {\left (\log \relax (3) - 3\right )}}{\log \relax (2)}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-exp((log(3)-3)/log(2))^4-4*x^3)/exp((log(3)-3)/log(2))^4,x, algorithm="maxima")

[Out]

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

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mupad [B]  time = 0.04, size = 20, normalized size = 0.87 \begin {gather*} -{\mathrm {e}}^{-\frac {\ln \left (81\right )-12}{\ln \relax (2)}}\,x^4-x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-exp(-(4*(log(3) - 3))/log(2))*(exp((4*(log(3) - 3))/log(2)) + 4*x^3),x)

[Out]

- x - x^4*exp(-(log(81) - 12)/log(2))

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sympy [A]  time = 0.06, size = 19, normalized size = 0.83 \begin {gather*} - \frac {x^{4} e^{\frac {12}{\log {\relax (2 )}}}}{3^{\frac {4}{\log {\relax (2 )}}}} - x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-exp((ln(3)-3)/ln(2))**4-4*x**3)/exp((ln(3)-3)/ln(2))**4,x)

[Out]

-3**(-4/log(2))*x**4*exp(12/log(2)) - x

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