3.97.64 \(\int \frac {10 x^2 \log ^3(x)+e^{\frac {144+72 x+9 x^2+e^4 x^2 \log ^2(x)}{x^2 \log ^2(x)}} (1440+720 x+90 x^2+(1440+360 x) \log (x)-10 x^2 \log ^3(x))}{x^5 \log ^3(x)-2 e^{\frac {144+72 x+9 x^2+e^4 x^2 \log ^2(x)}{x^2 \log ^2(x)}} x^5 \log ^3(x)+e^{\frac {2 (144+72 x+9 x^2+e^4 x^2 \log ^2(x))}{x^2 \log ^2(x)}} x^5 \log ^3(x)} \, dx\)

Optimal. Leaf size=33 \[ \frac {5}{x \left (-x+e^{e^4+\frac {9 (4+x)^2}{x^2 \log ^2(x)}} x\right )} \]

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Rubi [F]  time = 11.49, 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 {10 x^2 \log ^3(x)+\exp \left (\frac {144+72 x+9 x^2+e^4 x^2 \log ^2(x)}{x^2 \log ^2(x)}\right ) \left (1440+720 x+90 x^2+(1440+360 x) \log (x)-10 x^2 \log ^3(x)\right )}{x^5 \log ^3(x)-2 \exp \left (\frac {144+72 x+9 x^2+e^4 x^2 \log ^2(x)}{x^2 \log ^2(x)}\right ) x^5 \log ^3(x)+\exp \left (\frac {2 \left (144+72 x+9 x^2+e^4 x^2 \log ^2(x)\right )}{x^2 \log ^2(x)}\right ) x^5 \log ^3(x)} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(10*x^2*Log[x]^3 + E^((144 + 72*x + 9*x^2 + E^4*x^2*Log[x]^2)/(x^2*Log[x]^2))*(1440 + 720*x + 90*x^2 + (14
40 + 360*x)*Log[x] - 10*x^2*Log[x]^3))/(x^5*Log[x]^3 - 2*E^((144 + 72*x + 9*x^2 + E^4*x^2*Log[x]^2)/(x^2*Log[x
]^2))*x^5*Log[x]^3 + E^((2*(144 + 72*x + 9*x^2 + E^4*x^2*Log[x]^2))/(x^2*Log[x]^2))*x^5*Log[x]^3),x]

[Out]

10*Defer[Int][1/((-1 + E^(E^4 + (9*(4 + x)^2)/(x^2*Log[x]^2)))^2*x^3), x] - 10*Defer[Int][E^(E^4 + (9*(4 + x)^
2)/(x^2*Log[x]^2))/((-1 + E^(E^4 + (9*(4 + x)^2)/(x^2*Log[x]^2)))^2*x^3), x] + 1440*Defer[Int][E^(E^4 + (9*(4
+ x)^2)/(x^2*Log[x]^2))/((-1 + E^(E^4 + (9*(4 + x)^2)/(x^2*Log[x]^2)))^2*x^5*Log[x]^3), x] + 720*Defer[Int][E^
(E^4 + (9*(4 + x)^2)/(x^2*Log[x]^2))/((-1 + E^(E^4 + (9*(4 + x)^2)/(x^2*Log[x]^2)))^2*x^4*Log[x]^3), x] + 90*D
efer[Int][E^(E^4 + (9*(4 + x)^2)/(x^2*Log[x]^2))/((-1 + E^(E^4 + (9*(4 + x)^2)/(x^2*Log[x]^2)))^2*x^3*Log[x]^3
), x] + 1440*Defer[Int][E^(E^4 + (9*(4 + x)^2)/(x^2*Log[x]^2))/((-1 + E^(E^4 + (9*(4 + x)^2)/(x^2*Log[x]^2)))^
2*x^5*Log[x]^2), x] + 360*Defer[Int][E^(E^4 + (9*(4 + x)^2)/(x^2*Log[x]^2))/((-1 + E^(E^4 + (9*(4 + x)^2)/(x^2
*Log[x]^2)))^2*x^4*Log[x]^2), x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {10 x^2 \log ^3(x)+\exp \left (\frac {144+72 x+9 x^2+e^4 x^2 \log ^2(x)}{x^2 \log ^2(x)}\right ) \left (1440+720 x+90 x^2+(1440+360 x) \log (x)-10 x^2 \log ^3(x)\right )}{\left (1-e^{e^4+\frac {9 (4+x)^2}{x^2 \log ^2(x)}}\right )^2 x^5 \log ^3(x)} \, dx\\ &=\int \left (\frac {10}{\left (-1+e^{e^4+\frac {9 (4+x)^2}{x^2 \log ^2(x)}}\right )^2 x^3}-\frac {10 e^{e^4+\frac {9 (4+x)^2}{x^2 \log ^2(x)}}}{\left (-1+e^{e^4+\frac {9 (4+x)^2}{x^2 \log ^2(x)}}\right )^2 x^3}+\frac {1440 e^{e^4+\frac {9 (4+x)^2}{x^2 \log ^2(x)}}}{\left (-1+e^{e^4+\frac {9 (4+x)^2}{x^2 \log ^2(x)}}\right )^2 x^5 \log ^3(x)}+\frac {720 e^{e^4+\frac {9 (4+x)^2}{x^2 \log ^2(x)}}}{\left (-1+e^{e^4+\frac {9 (4+x)^2}{x^2 \log ^2(x)}}\right )^2 x^4 \log ^3(x)}+\frac {90 e^{e^4+\frac {9 (4+x)^2}{x^2 \log ^2(x)}}}{\left (-1+e^{e^4+\frac {9 (4+x)^2}{x^2 \log ^2(x)}}\right )^2 x^3 \log ^3(x)}+\frac {1440 e^{e^4+\frac {9 (4+x)^2}{x^2 \log ^2(x)}}}{\left (-1+e^{e^4+\frac {9 (4+x)^2}{x^2 \log ^2(x)}}\right )^2 x^5 \log ^2(x)}+\frac {360 e^{e^4+\frac {9 (4+x)^2}{x^2 \log ^2(x)}}}{\left (-1+e^{e^4+\frac {9 (4+x)^2}{x^2 \log ^2(x)}}\right )^2 x^4 \log ^2(x)}\right ) \, dx\\ &=10 \int \frac {1}{\left (-1+e^{e^4+\frac {9 (4+x)^2}{x^2 \log ^2(x)}}\right )^2 x^3} \, dx-10 \int \frac {e^{e^4+\frac {9 (4+x)^2}{x^2 \log ^2(x)}}}{\left (-1+e^{e^4+\frac {9 (4+x)^2}{x^2 \log ^2(x)}}\right )^2 x^3} \, dx+90 \int \frac {e^{e^4+\frac {9 (4+x)^2}{x^2 \log ^2(x)}}}{\left (-1+e^{e^4+\frac {9 (4+x)^2}{x^2 \log ^2(x)}}\right )^2 x^3 \log ^3(x)} \, dx+360 \int \frac {e^{e^4+\frac {9 (4+x)^2}{x^2 \log ^2(x)}}}{\left (-1+e^{e^4+\frac {9 (4+x)^2}{x^2 \log ^2(x)}}\right )^2 x^4 \log ^2(x)} \, dx+720 \int \frac {e^{e^4+\frac {9 (4+x)^2}{x^2 \log ^2(x)}}}{\left (-1+e^{e^4+\frac {9 (4+x)^2}{x^2 \log ^2(x)}}\right )^2 x^4 \log ^3(x)} \, dx+1440 \int \frac {e^{e^4+\frac {9 (4+x)^2}{x^2 \log ^2(x)}}}{\left (-1+e^{e^4+\frac {9 (4+x)^2}{x^2 \log ^2(x)}}\right )^2 x^5 \log ^3(x)} \, dx+1440 \int \frac {e^{e^4+\frac {9 (4+x)^2}{x^2 \log ^2(x)}}}{\left (-1+e^{e^4+\frac {9 (4+x)^2}{x^2 \log ^2(x)}}\right )^2 x^5 \log ^2(x)} \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.29, size = 29, normalized size = 0.88 \begin {gather*} \frac {5}{\left (-1+e^{e^4+\frac {9 (4+x)^2}{x^2 \log ^2(x)}}\right ) x^2} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(10*x^2*Log[x]^3 + E^((144 + 72*x + 9*x^2 + E^4*x^2*Log[x]^2)/(x^2*Log[x]^2))*(1440 + 720*x + 90*x^2
+ (1440 + 360*x)*Log[x] - 10*x^2*Log[x]^3))/(x^5*Log[x]^3 - 2*E^((144 + 72*x + 9*x^2 + E^4*x^2*Log[x]^2)/(x^2
*Log[x]^2))*x^5*Log[x]^3 + E^((2*(144 + 72*x + 9*x^2 + E^4*x^2*Log[x]^2))/(x^2*Log[x]^2))*x^5*Log[x]^3),x]

[Out]

5/((-1 + E^(E^4 + (9*(4 + x)^2)/(x^2*Log[x]^2)))*x^2)

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fricas [A]  time = 0.58, size = 43, normalized size = 1.30 \begin {gather*} \frac {5}{x^{2} e^{\left (\frac {x^{2} e^{4} \log \relax (x)^{2} + 9 \, x^{2} + 72 \, x + 144}{x^{2} \log \relax (x)^{2}}\right )} - x^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-10*x^2*log(x)^3+(360*x+1440)*log(x)+90*x^2+720*x+1440)*exp((x^2*exp(4)*log(x)^2+9*x^2+72*x+144)/x
^2/log(x)^2)+10*x^2*log(x)^3)/(x^5*log(x)^3*exp((x^2*exp(4)*log(x)^2+9*x^2+72*x+144)/x^2/log(x)^2)^2-2*x^5*log
(x)^3*exp((x^2*exp(4)*log(x)^2+9*x^2+72*x+144)/x^2/log(x)^2)+x^5*log(x)^3),x, algorithm="fricas")

[Out]

5/(x^2*e^((x^2*e^4*log(x)^2 + 9*x^2 + 72*x + 144)/(x^2*log(x)^2)) - x^2)

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giac [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \mathit {undef} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-10*x^2*log(x)^3+(360*x+1440)*log(x)+90*x^2+720*x+1440)*exp((x^2*exp(4)*log(x)^2+9*x^2+72*x+144)/x
^2/log(x)^2)+10*x^2*log(x)^3)/(x^5*log(x)^3*exp((x^2*exp(4)*log(x)^2+9*x^2+72*x+144)/x^2/log(x)^2)^2-2*x^5*log
(x)^3*exp((x^2*exp(4)*log(x)^2+9*x^2+72*x+144)/x^2/log(x)^2)+x^5*log(x)^3),x, algorithm="giac")

[Out]

undef

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maple [A]  time = 0.05, size = 39, normalized size = 1.18

method	result	size
risch	\(\frac {5}{x^{2} \left ({\mathrm e}^{\frac {x^{2} {\mathrm e}^{4} \ln \relax (x )^{2}+9 x^{2}+72 x +144}{x^{2} \ln \relax (x )^{2}}}-1\right )}\)	\(39\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((-10*x^2*ln(x)^3+(360*x+1440)*ln(x)+90*x^2+720*x+1440)*exp((x^2*exp(4)*ln(x)^2+9*x^2+72*x+144)/x^2/ln(x)^
2)+10*x^2*ln(x)^3)/(x^5*ln(x)^3*exp((x^2*exp(4)*ln(x)^2+9*x^2+72*x+144)/x^2/ln(x)^2)^2-2*x^5*ln(x)^3*exp((x^2*
exp(4)*ln(x)^2+9*x^2+72*x+144)/x^2/ln(x)^2)+x^5*ln(x)^3),x,method=_RETURNVERBOSE)

[Out]

5/x^2/(exp((x^2*exp(4)*ln(x)^2+9*x^2+72*x+144)/x^2/ln(x)^2)-1)

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maxima [A]  time = 0.50, size = 42, normalized size = 1.27 \begin {gather*} \frac {5}{x^{2} e^{\left (\frac {9}{\log \relax (x)^{2}} + \frac {72}{x \log \relax (x)^{2}} + \frac {144}{x^{2} \log \relax (x)^{2}} + e^{4}\right )} - x^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-10*x^2*log(x)^3+(360*x+1440)*log(x)+90*x^2+720*x+1440)*exp((x^2*exp(4)*log(x)^2+9*x^2+72*x+144)/x
^2/log(x)^2)+10*x^2*log(x)^3)/(x^5*log(x)^3*exp((x^2*exp(4)*log(x)^2+9*x^2+72*x+144)/x^2/log(x)^2)^2-2*x^5*log
(x)^3*exp((x^2*exp(4)*log(x)^2+9*x^2+72*x+144)/x^2/log(x)^2)+x^5*log(x)^3),x, algorithm="maxima")

[Out]

5/(x^2*e^(9/log(x)^2 + 72/(x*log(x)^2) + 144/(x^2*log(x)^2) + e^4) - x^2)

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mupad [B]  time = 6.21, size = 69, normalized size = 2.09 \begin {gather*} \frac {80\,\ln \relax (x)+x\,\left (20\,\ln \relax (x)+40\right )+5\,x^2+80}{x^2\,\left ({\mathrm {e}}^{{\mathrm {e}}^4+\frac {9}{{\ln \relax (x)}^2}+\frac {72}{x\,{\ln \relax (x)}^2}+\frac {144}{x^2\,{\ln \relax (x)}^2}}-1\right )\,\left (x+4\right )\,\left (x+4\,\ln \relax (x)+4\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((10*x^2*log(x)^3 + exp((72*x + 9*x^2 + x^2*exp(4)*log(x)^2 + 144)/(x^2*log(x)^2))*(720*x + log(x)*(360*x +
1440) - 10*x^2*log(x)^3 + 90*x^2 + 1440))/(x^5*log(x)^3 - 2*x^5*exp((72*x + 9*x^2 + x^2*exp(4)*log(x)^2 + 144
)/(x^2*log(x)^2))*log(x)^3 + x^5*exp((2*(72*x + 9*x^2 + x^2*exp(4)*log(x)^2 + 144))/(x^2*log(x)^2))*log(x)^3),
x)

[Out]

(80*log(x) + x*(20*log(x) + 40) + 5*x^2 + 80)/(x^2*(exp(exp(4) + 9/log(x)^2 + 72/(x*log(x)^2) + 144/(x^2*log(x
)^2)) - 1)*(x + 4)*(x + 4*log(x) + 4))

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sympy [A]  time = 0.39, size = 39, normalized size = 1.18 \begin {gather*} \frac {5}{x^{2} e^{\frac {x^{2} e^{4} \log {\relax (x )}^{2} + 9 x^{2} + 72 x + 144}{x^{2} \log {\relax (x )}^{2}}} - x^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-10*x**2*ln(x)**3+(360*x+1440)*ln(x)+90*x**2+720*x+1440)*exp((x**2*exp(4)*ln(x)**2+9*x**2+72*x+144
)/x**2/ln(x)**2)+10*x**2*ln(x)**3)/(x**5*ln(x)**3*exp((x**2*exp(4)*ln(x)**2+9*x**2+72*x+144)/x**2/ln(x)**2)**2
-2*x**5*ln(x)**3*exp((x**2*exp(4)*ln(x)**2+9*x**2+72*x+144)/x**2/ln(x)**2)+x**5*ln(x)**3),x)

[Out]

5/(x**2*exp((x**2*exp(4)*log(x)**2 + 9*x**2 + 72*x + 144)/(x**2*log(x)**2)) - x**2)

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