3.81.50 \(\int e^{25-19 x+(25-19 x) \log (81 x^4)} (102 x-95 x^2-19 x^2 \log (81 x^4)) \, dx\)

Optimal. Leaf size=24 \[ e^{(5 (5-4 x)+x) \left (1+\log \left (81 x^4\right )\right )} x^2 \]

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Rubi [F]  time = 0.55, 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 e^{25-19 x+(25-19 x) \log \left (81 x^4\right )} \left (102 x-95 x^2-19 x^2 \log \left (81 x^4\right )\right ) \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[E^(25 - 19*x + (25 - 19*x)*Log[81*x^4])*(102*x - 95*x^2 - 19*x^2*Log[81*x^4]),x]

[Out]

102*Defer[Int][x/E^((-25 + 19*x)*(1 + Log[81*x^4])), x] - 95*Defer[Int][x^2/E^((-25 + 19*x)*(1 + Log[81*x^4]))
, x] - 19*Defer[Int][(x^2*Log[81*x^4])/E^((-25 + 19*x)*(1 + Log[81*x^4])), x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int e^{-\left ((-25+19 x) \left (1+\log \left (81 x^4\right )\right )\right )} \left (102 x-95 x^2-19 x^2 \log \left (81 x^4\right )\right ) \, dx\\ &=\int \left (102 e^{-\left ((-25+19 x) \left (1+\log \left (81 x^4\right )\right )\right )} x-95 e^{-\left ((-25+19 x) \left (1+\log \left (81 x^4\right )\right )\right )} x^2-19 e^{-\left ((-25+19 x) \left (1+\log \left (81 x^4\right )\right )\right )} x^2 \log \left (81 x^4\right )\right ) \, dx\\ &=-\left (19 \int e^{-\left ((-25+19 x) \left (1+\log \left (81 x^4\right )\right )\right )} x^2 \log \left (81 x^4\right ) \, dx\right )-95 \int e^{-\left ((-25+19 x) \left (1+\log \left (81 x^4\right )\right )\right )} x^2 \, dx+102 \int e^{-\left ((-25+19 x) \left (1+\log \left (81 x^4\right )\right )\right )} x \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.49, size = 20, normalized size = 0.83 \begin {gather*} (81 e)^{25-19 x} x^{102} \left (x^4\right )^{-19 x} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[E^(25 - 19*x + (25 - 19*x)*Log[81*x^4])*(102*x - 95*x^2 - 19*x^2*Log[81*x^4]),x]

[Out]

((81*E)^(25 - 19*x)*x^102)/(x^4)^(19*x)

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fricas [A]  time = 0.64, size = 23, normalized size = 0.96 \begin {gather*} x^{2} e^{\left (-{\left (19 \, x - 25\right )} \log \left (81 \, x^{4}\right ) - 19 \, x + 25\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-19*x^2*log(81*x^4)-95*x^2+102*x)*exp((-19*x+25)*log(81*x^4)-19*x+25),x, algorithm="fricas")

[Out]

x^2*e^(-(19*x - 25)*log(81*x^4) - 19*x + 25)

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giac [A]  time = 0.29, size = 27, normalized size = 1.12 \begin {gather*} x^{2} e^{\left (-19 \, x \log \left (81 \, x^{4}\right ) - 19 \, x + 25 \, \log \left (81 \, x^{4}\right ) + 25\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-19*x^2*log(81*x^4)-95*x^2+102*x)*exp((-19*x+25)*log(81*x^4)-19*x+25),x, algorithm="giac")

[Out]

x^2*e^(-19*x*log(81*x^4) - 19*x + 25*log(81*x^4) + 25)

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maple [A]  time = 0.05, size = 22, normalized size = 0.92

method	result	size
risch	\(x^{2} \left (81 x^{4}\right )^{-19 x +25} {\mathrm e}^{-19 x +25}\)	\(22\)
default	\(x^{2} {\mathrm e}^{\left (-19 x +25\right ) \ln \left (81 x^{4}\right )-19 x +25}\)	\(23\)
norman	\(x^{2} {\mathrm e}^{\left (-19 x +25\right ) \ln \left (81 x^{4}\right )-19 x +25}\)	\(23\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((-19*x^2*ln(81*x^4)-95*x^2+102*x)*exp((-19*x+25)*ln(81*x^4)-19*x+25),x,method=_RETURNVERBOSE)

[Out]

x^2*(81*x^4)^(-19*x+25)*exp(-19*x+25)

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maxima [A]  time = 0.52, size = 21, normalized size = 0.88 \begin {gather*} 515377520732011331036461129765621272702107522001 \, x^{102} e^{\left (-76 \, x \log \relax (3) - 76 \, x \log \relax (x) - 19 \, x + 25\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-19*x^2*log(81*x^4)-95*x^2+102*x)*exp((-19*x+25)*log(81*x^4)-19*x+25),x, algorithm="maxima")

[Out]

515377520732011331036461129765621272702107522001*x^102*e^(-76*x*log(3) - 76*x*log(x) - 19*x + 25)

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mupad [B]  time = 5.52, size = 27, normalized size = 1.12 \begin {gather*} \frac {515377520732011331036461129765621272702107522001\,x^{102}\,{\mathrm {e}}^{-19\,x}\,{\mathrm {e}}^{25}}{3^{76\,x}\,{\left (x^4\right )}^{19\,x}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-exp(25 - log(81*x^4)*(19*x - 25) - 19*x)*(95*x^2 - 102*x + 19*x^2*log(81*x^4)),x)

[Out]

(515377520732011331036461129765621272702107522001*x^102*exp(-19*x)*exp(25))/(3^(76*x)*(x^4)^(19*x))

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sympy [A]  time = 0.51, size = 20, normalized size = 0.83 \begin {gather*} x^{2} e^{- 19 x + \left (25 - 19 x\right ) \log {\left (81 x^{4} \right )} + 25} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-19*x**2*ln(81*x**4)-95*x**2+102*x)*exp((-19*x+25)*ln(81*x**4)-19*x+25),x)

[Out]

x**2*exp(-19*x + (25 - 19*x)*log(81*x**4) + 25)

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