3.35.96 \(\int \frac {1}{3} e^{-3-x+x^3-x^2 \log (x)} (25-23 x-26 x^2+74 x^3+3 x^4+(-50 x^2-2 x^3) \log (x)) \, dx\)

Optimal. Leaf size=25 \[ \frac {1}{3} e^{-3-x+x^2 (x-\log (x))} x (25+x) \]

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Rubi [F]  time = 1.51, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \int \frac {1}{3} e^{-3-x+x^3-x^2 \log (x)} \left (25-23 x-26 x^2+74 x^3+3 x^4+\left (-50 x^2-2 x^3\right ) \log (x)\right ) \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(E^(-3 - x + x^3 - x^2*Log[x])*(25 - 23*x - 26*x^2 + 74*x^3 + 3*x^4 + (-50*x^2 - 2*x^3)*Log[x]))/3,x]

[Out]

(25*Defer[Int][E^(-3 - x + x^3 - x^2*Log[x]), x])/3 - (23*Defer[Int][E^(-3 - x + x^3 - x^2*Log[x])*x, x])/3 -
(26*Defer[Int][E^(-3 - x + x^3 - x^2*Log[x])*x^2, x])/3 + (74*Defer[Int][E^(-3 - x + x^3 - x^2*Log[x])*x^3, x]
)/3 + Defer[Int][E^(-3 - x + x^3 - x^2*Log[x])*x^4, x] - (50*Defer[Int][E^(-3 - x + x^3 - x^2*Log[x])*x^2*Log[
x], x])/3 - (2*Defer[Int][E^(-3 - x + x^3 - x^2*Log[x])*x^3*Log[x], x])/3

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{3} \int e^{-3-x+x^3-x^2 \log (x)} \left (25-23 x-26 x^2+74 x^3+3 x^4+\left (-50 x^2-2 x^3\right ) \log (x)\right ) \, dx\\ &=\frac {1}{3} \int \left (25 e^{-3-x+x^3-x^2 \log (x)}-23 e^{-3-x+x^3-x^2 \log (x)} x-26 e^{-3-x+x^3-x^2 \log (x)} x^2+74 e^{-3-x+x^3-x^2 \log (x)} x^3+3 e^{-3-x+x^3-x^2 \log (x)} x^4-2 e^{-3-x+x^3-x^2 \log (x)} x^2 (25+x) \log (x)\right ) \, dx\\ &=-\left (\frac {2}{3} \int e^{-3-x+x^3-x^2 \log (x)} x^2 (25+x) \log (x) \, dx\right )-\frac {23}{3} \int e^{-3-x+x^3-x^2 \log (x)} x \, dx+\frac {25}{3} \int e^{-3-x+x^3-x^2 \log (x)} \, dx-\frac {26}{3} \int e^{-3-x+x^3-x^2 \log (x)} x^2 \, dx+\frac {74}{3} \int e^{-3-x+x^3-x^2 \log (x)} x^3 \, dx+\int e^{-3-x+x^3-x^2 \log (x)} x^4 \, dx\\ &=-\left (\frac {2}{3} \int \left (25 e^{-3-x+x^3-x^2 \log (x)} x^2 \log (x)+e^{-3-x+x^3-x^2 \log (x)} x^3 \log (x)\right ) \, dx\right )-\frac {23}{3} \int e^{-3-x+x^3-x^2 \log (x)} x \, dx+\frac {25}{3} \int e^{-3-x+x^3-x^2 \log (x)} \, dx-\frac {26}{3} \int e^{-3-x+x^3-x^2 \log (x)} x^2 \, dx+\frac {74}{3} \int e^{-3-x+x^3-x^2 \log (x)} x^3 \, dx+\int e^{-3-x+x^3-x^2 \log (x)} x^4 \, dx\\ &=-\left (\frac {2}{3} \int e^{-3-x+x^3-x^2 \log (x)} x^3 \log (x) \, dx\right )-\frac {23}{3} \int e^{-3-x+x^3-x^2 \log (x)} x \, dx+\frac {25}{3} \int e^{-3-x+x^3-x^2 \log (x)} \, dx-\frac {26}{3} \int e^{-3-x+x^3-x^2 \log (x)} x^2 \, dx-\frac {50}{3} \int e^{-3-x+x^3-x^2 \log (x)} x^2 \log (x) \, dx+\frac {74}{3} \int e^{-3-x+x^3-x^2 \log (x)} x^3 \, dx+\int e^{-3-x+x^3-x^2 \log (x)} x^4 \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.95, size = 26, normalized size = 1.04 \begin {gather*} \frac {1}{3} e^{-3-x+x^3} x^{1-x^2} (25+x) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(E^(-3 - x + x^3 - x^2*Log[x])*(25 - 23*x - 26*x^2 + 74*x^3 + 3*x^4 + (-50*x^2 - 2*x^3)*Log[x]))/3,x
]

[Out]

(E^(-3 - x + x^3)*x^(1 - x^2)*(25 + x))/3

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fricas [A]  time = 0.57, size = 25, normalized size = 1.00 \begin {gather*} \frac {1}{3} \, {\left (x^{2} + 25 \, x\right )} e^{\left (x^{3} - x^{2} \log \relax (x) - x - 3\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/3*((-2*x^3-50*x^2)*log(x)+3*x^4+74*x^3-26*x^2-23*x+25)/exp(x^2*log(x)-x^3+x+3),x, algorithm="frica
s")

[Out]

1/3*(x^2 + 25*x)*e^(x^3 - x^2*log(x) - x - 3)

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giac [A]  time = 0.17, size = 42, normalized size = 1.68 \begin {gather*} \frac {1}{3} \, {\left (x^{2} e^{\left (x^{3} - x^{2} \log \relax (x) - x\right )} + 25 \, x e^{\left (x^{3} - x^{2} \log \relax (x) - x\right )}\right )} e^{\left (-3\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/3*((-2*x^3-50*x^2)*log(x)+3*x^4+74*x^3-26*x^2-23*x+25)/exp(x^2*log(x)-x^3+x+3),x, algorithm="giac"
)

[Out]

1/3*(x^2*e^(x^3 - x^2*log(x) - x) + 25*x*e^(x^3 - x^2*log(x) - x))*e^(-3)

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maple [A]  time = 0.03, size = 23, normalized size = 0.92

method	result	size
risch	\(\frac {x \left (x +25\right ) x^{-x^{2}} {\mathrm e}^{x^{3}-x -3}}{3}\)	\(23\)
norman	\(\left (\frac {25}{3} x +\frac {1}{3} x^{2}\right ) {\mathrm e}^{-x^{2} \ln \relax (x )+x^{3}-x -3}\)	\(28\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/3*((-2*x^3-50*x^2)*ln(x)+3*x^4+74*x^3-26*x^2-23*x+25)/exp(x^2*ln(x)-x^3+x+3),x,method=_RETURNVERBOSE)

[Out]

1/3*x*(x+25)/(x^(x^2))*exp(x^3-x-3)

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maxima [A]  time = 0.51, size = 25, normalized size = 1.00 \begin {gather*} \frac {1}{3} \, {\left (x^{2} + 25 \, x\right )} e^{\left (x^{3} - x^{2} \log \relax (x) - x - 3\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/3*((-2*x^3-50*x^2)*log(x)+3*x^4+74*x^3-26*x^2-23*x+25)/exp(x^2*log(x)-x^3+x+3),x, algorithm="maxim
a")

[Out]

1/3*(x^2 + 25*x)*e^(x^3 - x^2*log(x) - x - 3)

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mupad [B]  time = 2.16, size = 23, normalized size = 0.92 \begin {gather*} \frac {x^{1-x^2}\,{\mathrm {e}}^{x^3-x-3}\,\left (x+25\right )}{3} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-exp(x^3 - x^2*log(x) - x - 3)*((23*x)/3 + (log(x)*(50*x^2 + 2*x^3))/3 + (26*x^2)/3 - (74*x^3)/3 - x^4 - 2
5/3),x)

[Out]

(x^(1 - x^2)*exp(x^3 - x - 3)*(x + 25))/3

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sympy [A]  time = 0.35, size = 22, normalized size = 0.88 \begin {gather*} \frac {\left (x^{2} + 25 x\right ) e^{x^{3} - x^{2} \log {\relax (x )} - x - 3}}{3} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/3*((-2*x**3-50*x**2)*ln(x)+3*x**4+74*x**3-26*x**2-23*x+25)/exp(x**2*ln(x)-x**3+x+3),x)

[Out]

(x**2 + 25*x)*exp(x**3 - x**2*log(x) - x - 3)/3

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