3.55.8 \(\int \frac {20736 x^2+1440 x^3+25 x^4+13824 x^5+480 x^6+2304 x^8+e^x (-720+670 x+25 x^2-960 x^3+240 x^4) \log (3)}{20736 x^2+1440 x^3+25 x^4+13824 x^5+480 x^6+2304 x^8} \, dx\)

Optimal. Leaf size=24 \[ x+\frac {e^x \log (3)}{x \left (x+\frac {48}{5} \left (3+x^3\right )\right )} \]

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Rubi [F]  time = 0.00, 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*} \text {\$Aborted} \end {gather*}

Verification is not applicable to the result.

[In]

Int[(20736*x^2 + 1440*x^3 + 25*x^4 + 13824*x^5 + 480*x^6 + 2304*x^8 + E^x*(-720 + 670*x + 25*x^2 - 960*x^3 + 2
40*x^4)*Log[3])/(20736*x^2 + 1440*x^3 + 25*x^4 + 13824*x^5 + 480*x^6 + 2304*x^8),x]

[Out]

$Aborted

Rubi steps

Aborted

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Mathematica [A]  time = 0.10, size = 24, normalized size = 1.00 \begin {gather*} x+\frac {5 e^x \log (3)}{x \left (144+5 x+48 x^3\right )} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(20736*x^2 + 1440*x^3 + 25*x^4 + 13824*x^5 + 480*x^6 + 2304*x^8 + E^x*(-720 + 670*x + 25*x^2 - 960*x
^3 + 240*x^4)*Log[3])/(20736*x^2 + 1440*x^3 + 25*x^4 + 13824*x^5 + 480*x^6 + 2304*x^8),x]

[Out]

x + (5*E^x*Log[3])/(x*(144 + 5*x + 48*x^3))

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fricas [A]  time = 0.59, size = 39, normalized size = 1.62 \begin {gather*} \frac {48 \, x^{5} + 5 \, x^{3} + 144 \, x^{2} + 5 \, e^{x} \log \relax (3)}{48 \, x^{4} + 5 \, x^{2} + 144 \, x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((240*x^4-960*x^3+25*x^2+670*x-720)*log(3)*exp(x)+2304*x^8+480*x^6+13824*x^5+25*x^4+1440*x^3+20736*x
^2)/(2304*x^8+480*x^6+13824*x^5+25*x^4+1440*x^3+20736*x^2),x, algorithm="fricas")

[Out]

(48*x^5 + 5*x^3 + 144*x^2 + 5*e^x*log(3))/(48*x^4 + 5*x^2 + 144*x)

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giac [A]  time = 0.18, size = 39, normalized size = 1.62 \begin {gather*} \frac {48 \, x^{5} + 5 \, x^{3} + 144 \, x^{2} + 5 \, e^{x} \log \relax (3)}{48 \, x^{4} + 5 \, x^{2} + 144 \, x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((240*x^4-960*x^3+25*x^2+670*x-720)*log(3)*exp(x)+2304*x^8+480*x^6+13824*x^5+25*x^4+1440*x^3+20736*x
^2)/(2304*x^8+480*x^6+13824*x^5+25*x^4+1440*x^3+20736*x^2),x, algorithm="giac")

[Out]

(48*x^5 + 5*x^3 + 144*x^2 + 5*e^x*log(3))/(48*x^4 + 5*x^2 + 144*x)

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maple [A]  time = 0.18, size = 24, normalized size = 1.00

method	result	size
risch	\(x +\frac {5 \ln \relax (3) {\mathrm e}^{x}}{x \left (48 x^{3}+5 x +144\right )}\)	\(24\)
norman	\(\frac {-\frac {20736 x}{5}-\frac {6912 x^{4}}{5}+5 x^{3}+48 x^{5}+5 \ln \relax (3) {\mathrm e}^{x}}{x \left (48 x^{3}+5 x +144\right )}\)	\(42\)
default	\(\frac {-\frac {155520}{6718589} x^{2}+\frac {6718464}{6718589} x -\frac {10800}{6718589}}{x^{3}+\frac {5}{48} x +3}+\frac {2985984 \left (\munderset {\textit {\_R} =\RootOf \left (48 \textit {\_Z}^{3}+5 \textit {\_Z} +144\right )}{\sum }\frac {\left (-5 \textit {\_R} +432\right ) \ln \left (x -\textit {\_R} \right )}{144 \textit {\_R}^{2}+5}\right )}{6718589}+\frac {\frac {466560}{6718589} x^{2}+\frac {375}{6718589} x +\frac {32400}{6718589}}{x^{3}+\frac {5}{48} x +3}+\frac {1440 \left (\munderset {\textit {\_R} =\RootOf \left (48 \textit {\_Z}^{3}+5 \textit {\_Z} +144\right )}{\sum }\frac {\left (15552 \textit {\_R} +25\right ) \ln \left (x -\textit {\_R} \right )}{144 \textit {\_R}^{2}+5}\right )}{6718589}+\frac {\frac {625}{644984544} x^{2}-\frac {1125}{26874356} x -\frac {24300}{6718589}}{x^{3}+\frac {5}{48} x +3}+\frac {125 \left (\munderset {\textit {\_R} =\RootOf \left (48 \textit {\_Z}^{3}+5 \textit {\_Z} +144\right )}{\sum }\frac {\left (5 \textit {\_R} -432\right ) \ln \left (x -\textit {\_R} \right )}{144 \textit {\_R}^{2}+5}\right )}{13437178}+\frac {-\frac {155520}{6718589} x^{2}-\frac {13437303}{6718589} x -\frac {10800}{6718589}}{x^{3}+\frac {5}{48} x +3}+\frac {-\frac {22395505}{322492272} x^{2}+\frac {375}{13437178} x +\frac {16200}{6718589}}{x^{3}+\frac {5}{48} x +3}+\frac {5 \left (\munderset {\textit {\_R} =\RootOf \left (48 \textit {\_Z}^{3}+5 \textit {\_Z} +144\right )}{\sum }\frac {\left (8958077 \textit {\_R} +3600\right ) \ln \left (x -\textit {\_R} \right )}{144 \textit {\_R}^{2}+5}\right )}{6718589}+x -\frac {-\frac {29860465}{644984544} x^{2}-\frac {26874231}{26874356} x +\frac {2700}{6718589}}{x^{3}+\frac {5}{48} x +3}-\frac {3 \left (\munderset {\textit {\_R} =\RootOf \left (48 \textit {\_Z}^{3}+5 \textit {\_Z} +144\right )}{\sum }\frac {\left (34837105 \textit {\_R} [phone]\right ) \ln \left (x -\textit {\_R} \right )}{144 \textit {\_R}^{2}+5}\right )}{13437178}+\frac {5 \ln \relax (3) {\mathrm e}^{x}}{x \left (48 x^{3}+5 x +144\right )}+\frac {5 \ln \relax (3) \left (\munderset {\textit {\_R1} =\RootOf \left (48 \textit {\_Z}^{3}+5 \textit {\_Z} +144\right )}{\sum }\frac {\left (9352563888 \textit {\_R1}^{2}-30971987712 \textit {\_R1} [phone]\right ) {\mathrm e}^{\textit {\_R1}} \expIntegralEi \left (1, -x +\textit {\_R1} \right )}{144 \textit {\_R1}^{2}+5}\right )}{69658330752}+\frac {335 \ln \relax (3) \left (\munderset {\textit {\_R1} =\RootOf \left (48 \textit {\_Z}^{3}+5 \textit {\_Z} +144\right )}{\sum }\frac {\left (322665072 \textit {\_R1}^{2}-7637760 \textit {\_R1} [phone]\right ) {\mathrm e}^{\textit {\_R1}} \expIntegralEi \left (1, -x +\textit {\_R1} \right )}{144 \textit {\_R1}^{2}+5}\right )}{69658330752}-\frac {25 \ln \relax (3) \left (\munderset {\textit {\_R1} =\RootOf \left (48 \textit {\_Z}^{3}+5 \textit {\_Z} +144\right )}{\sum }\frac {\left (360 \textit {\_R1}^{2}-15912 \textit {\_R1} +31129\right ) {\mathrm e}^{\textit {\_R1}} \expIntegralEi \left (1, -x +\textit {\_R1} \right )}{144 \textit {\_R1}^{2}+5}\right )}{6718589}+\frac {120 \ln \relax (3) \left (\munderset {\textit {\_R1} =\RootOf \left (48 \textit {\_Z}^{3}+5 \textit {\_Z} +144\right )}{\sum }\frac {\left (25 \textit {\_R1}^{2}-1105 \textit {\_R1} -91152\right ) {\mathrm e}^{\textit {\_R1}} \expIntegralEi \left (1, -x +\textit {\_R1} \right )}{144 \textit {\_R1}^{2}+5}\right )}{6718589}-\frac {480 \ln \relax (3) \left (\munderset {\textit {\_R1} =\RootOf \left (48 \textit {\_Z}^{3}+5 \textit {\_Z} +144\right )}{\sum }\frac {\left (31104 \textit {\_R1}^{2}-31079 \textit {\_R1} +2110\right ) {\mathrm e}^{\textit {\_R1}} \expIntegralEi \left (1, -x +\textit {\_R1} \right )}{144 \textit {\_R1}^{2}+5}\right )}{6718589}\)	\(576\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((240*x^4-960*x^3+25*x^2+670*x-720)*ln(3)*exp(x)+2304*x^8+480*x^6+13824*x^5+25*x^4+1440*x^3+20736*x^2)/(23
04*x^8+480*x^6+13824*x^5+25*x^4+1440*x^3+20736*x^2),x,method=_RETURNVERBOSE)

[Out]

x+5*ln(3)*exp(x)/x/(48*x^3+5*x+144)

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maxima [A]  time = 0.45, size = 39, normalized size = 1.62 \begin {gather*} \frac {48 \, x^{5} + 5 \, x^{3} + 144 \, x^{2} + 5 \, e^{x} \log \relax (3)}{48 \, x^{4} + 5 \, x^{2} + 144 \, x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((240*x^4-960*x^3+25*x^2+670*x-720)*log(3)*exp(x)+2304*x^8+480*x^6+13824*x^5+25*x^4+1440*x^3+20736*x
^2)/(2304*x^8+480*x^6+13824*x^5+25*x^4+1440*x^3+20736*x^2),x, algorithm="maxima")

[Out]

(48*x^5 + 5*x^3 + 144*x^2 + 5*e^x*log(3))/(48*x^4 + 5*x^2 + 144*x)

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mupad [B]  time = 3.70, size = 23, normalized size = 0.96 \begin {gather*} x+\frac {5\,{\mathrm {e}}^x\,\ln \relax (3)}{x\,\left (48\,x^3+5\,x+144\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((20736*x^2 + 1440*x^3 + 25*x^4 + 13824*x^5 + 480*x^6 + 2304*x^8 + exp(x)*log(3)*(670*x + 25*x^2 - 960*x^3
+ 240*x^4 - 720))/(20736*x^2 + 1440*x^3 + 25*x^4 + 13824*x^5 + 480*x^6 + 2304*x^8),x)

[Out]

x + (5*exp(x)*log(3))/(x*(5*x + 48*x^3 + 144))

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sympy [A]  time = 0.20, size = 22, normalized size = 0.92 \begin {gather*} x + \frac {5 e^{x} \log {\relax (3 )}}{48 x^{4} + 5 x^{2} + 144 x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((240*x**4-960*x**3+25*x**2+670*x-720)*ln(3)*exp(x)+2304*x**8+480*x**6+13824*x**5+25*x**4+1440*x**3+
20736*x**2)/(2304*x**8+480*x**6+13824*x**5+25*x**4+1440*x**3+20736*x**2),x)

[Out]

x + 5*exp(x)*log(3)/(48*x**4 + 5*x**2 + 144*x)

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