\(\int e^{25-19 x+(25-19 x) \log (81 x^4)} (102 x-95 x^2-19 x^2 \log (81 x^4)) \, dx\) [8050]

Optimal result

Integrand size = 40, antiderivative size = 24 \[ \int e^{25-19 x+(25-19 x) \log \left (81 x^4\right )} \left (102 x-95 x^2-19 x^2 \log \left (81 x^4\right )\right ) \, dx=e^{(5 (5-4 x)+x) \left (1+\log \left (81 x^4\right )\right )} x^2 \]

[Out]

exp((-19*x+25)*(ln(81*x^4)+1))*x^2

Rubi [F]

\[ \int e^{25-19 x+(25-19 x) \log \left (81 x^4\right )} \left (102 x-95 x^2-19 x^2 \log \left (81 x^4\right )\right ) \, dx=\int e^{25-19 x+(25-19 x) \log \left (81 x^4\right )} \left (102 x-95 x^2-19 x^2 \log \left (81 x^4\right )\right ) \, dx \]

[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{align*} \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{align*}

Mathematica [F]

\[ \int e^{25-19 x+(25-19 x) \log \left (81 x^4\right )} \left (102 x-95 x^2-19 x^2 \log \left (81 x^4\right )\right ) \, dx=\int e^{25-19 x+(25-19 x) \log \left (81 x^4\right )} \left (102 x-95 x^2-19 x^2 \log \left (81 x^4\right )\right ) \, dx \]

[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]

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]

Maple [A] (verified)

Time = 0.17 (sec) , antiderivative size = 22, normalized size of antiderivative = 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	\(x^{2} {\mathrm e}^{\left (-19 x +25\right ) \ln \left (81 x^{4}\right )-19 x +25}\)	\(23\)
parallelrisch	\(x^{2} {\mathrm e}^{\left (-19 x +25\right ) \ln \left (81 x^{4}\right )-19 x +25}\)	\(23\)

[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)

Fricas [A] (verification not implemented)

none

Time = 0.28 (sec) , antiderivative size = 23, normalized size of antiderivative = 0.96 \[ \int e^{25-19 x+(25-19 x) \log \left (81 x^4\right )} \left (102 x-95 x^2-19 x^2 \log \left (81 x^4\right )\right ) \, dx=x^{2} e^{\left (-{\left (19 \, x - 25\right )} \log \left (81 \, x^{4}\right ) - 19 \, x + 25\right )} \]

[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)

Sympy [A] (verification not implemented)

Time = 0.10 (sec) , antiderivative size = 20, normalized size of antiderivative = 0.83 \[ \int e^{25-19 x+(25-19 x) \log \left (81 x^4\right )} \left (102 x-95 x^2-19 x^2 \log \left (81 x^4\right )\right ) \, dx=x^{2} e^{- 19 x + \left (25 - 19 x\right ) \log {\left (81 x^{4} \right )} + 25} \]

[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)

Maxima [A] (verification not implemented)

none

Time = 0.33 (sec) , antiderivative size = 21, normalized size of antiderivative = 0.88 \[ \int e^{25-19 x+(25-19 x) \log \left (81 x^4\right )} \left (102 x-95 x^2-19 x^2 \log \left (81 x^4\right )\right ) \, dx=515377520732011331036461129765621272702107522001 \, x^{102} e^{\left (-76 \, x \log \left (3\right ) - 76 \, x \log \left (x\right ) - 19 \, x + 25\right )} \]

[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)

Giac [A] (verification not implemented)

none

Time = 0.35 (sec) , antiderivative size = 27, normalized size of antiderivative = 1.12 \[ \int e^{25-19 x+(25-19 x) \log \left (81 x^4\right )} \left (102 x-95 x^2-19 x^2 \log \left (81 x^4\right )\right ) \, dx=x^{2} e^{\left (-19 \, x \log \left (81 \, x^{4}\right ) - 19 \, x + 25 \, \log \left (81 \, x^{4}\right ) + 25\right )} \]

[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)

Mupad [B] (verification not implemented)

Time = 13.35 (sec) , antiderivative size = 27, normalized size of antiderivative = 1.12 \[ \int e^{25-19 x+(25-19 x) \log \left (81 x^4\right )} \left (102 x-95 x^2-19 x^2 \log \left (81 x^4\right )\right ) \, dx=\frac {515377520732011331036461129765621272702107522001\,x^{102}\,{\mathrm {e}}^{-19\,x}\,{\mathrm {e}}^{25}}{3^{76\,x}\,{\left (x^4\right )}^{19\,x}} \]

[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))