Optimal. Leaf size=29 \[ e^{\frac {-1+\log (5)}{\log \left (-e^{x+\frac {25 (3+x)}{3+\log (x)}}+x\right )}} \]
[Out]
________________________________________________________________________________________
Rubi [F]
time = 34.50, 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 {\exp \left (\frac {-1+\log (5)}{\log \left (-e^{\frac {75+28 x+x \log (x)}{3+\log (x)}}+x\right )}\right ) \left (-9 x+9 x \log (5)+(-6 x+6 x \log (5)) \log (x)+(-x+x \log (5)) \log ^2(x)+e^{\frac {75+28 x+x \log (x)}{3+\log (x)}} \left (-75+59 x+(75-59 x) \log (5)+(31 x-31 x \log (5)) \log (x)+(x-x \log (5)) \log ^2(x)\right )\right )}{\left (-9 x^2-6 x^2 \log (x)-x^2 \log ^2(x)+e^{\frac {75+28 x+x \log (x)}{3+\log (x)}} \left (9 x+6 x \log (x)+x \log ^2(x)\right )\right ) \log ^2\left (-e^{\frac {75+28 x+x \log (x)}{3+\log (x)}}+x\right )} \, dx \end {gather*}
Verification is not applicable to the result.
[In]
[Out]
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {\exp \left (\frac {-1+\log (5)}{\log \left (-e^{\frac {75+28 x+x \log (x)}{3+\log (x)}}+x\right )}\right ) \left (x (-9+9 \log (5))+(-6 x+6 x \log (5)) \log (x)+(-x+x \log (5)) \log ^2(x)+e^{\frac {75+28 x+x \log (x)}{3+\log (x)}} \left (-75+59 x+(75-59 x) \log (5)+(31 x-31 x \log (5)) \log (x)+(x-x \log (5)) \log ^2(x)\right )\right )}{\left (-9 x^2-6 x^2 \log (x)-x^2 \log ^2(x)+e^{\frac {75+28 x+x \log (x)}{3+\log (x)}} \left (9 x+6 x \log (x)+x \log ^2(x)\right )\right ) \log ^2\left (-e^{\frac {75+28 x+x \log (x)}{3+\log (x)}}+x\right )} \, dx\\ &=\int \frac {\left (\frac {5}{e}\right )^{\frac {1}{\log \left (-e^{\frac {75+28 x+x \log (x)}{3+\log (x)}}+x\right )}} (1-\log (5)) \left (9 x+6 x \log (x)+x \log ^2(x)-e^{\frac {75+28 x}{3+\log (x)}} x^{\frac {x}{3+\log (x)}} \left (-75+59 x+31 x \log (x)+x \log ^2(x)\right )\right )}{x \left (x-e^{\frac {75+28 x}{3+\log (x)}} x^{\frac {x}{3+\log (x)}}\right ) (3+\log (x))^2 \log ^2\left (-e^{\frac {75+28 x+x \log (x)}{3+\log (x)}}+x\right )} \, dx\\ &=(1-\log (5)) \int \frac {\left (\frac {5}{e}\right )^{\frac {1}{\log \left (-e^{\frac {75+28 x+x \log (x)}{3+\log (x)}}+x\right )}} \left (9 x+6 x \log (x)+x \log ^2(x)-e^{\frac {75+28 x}{3+\log (x)}} x^{\frac {x}{3+\log (x)}} \left (-75+59 x+31 x \log (x)+x \log ^2(x)\right )\right )}{x \left (x-e^{\frac {75+28 x}{3+\log (x)}} x^{\frac {x}{3+\log (x)}}\right ) (3+\log (x))^2 \log ^2\left (-e^{\frac {75+28 x+x \log (x)}{3+\log (x)}}+x\right )} \, dx\\ &=(1-\log (5)) \int \left (\frac {\left (\frac {5}{e}\right )^{\frac {1}{\log \left (-e^{\frac {75+28 x+x \log (x)}{3+\log (x)}}+x\right )}} \left (-75+59 x+31 x \log (x)+x \log ^2(x)\right )}{x (3+\log (x))^2 \log ^2\left (-e^{\frac {75+28 x+x \log (x)}{3+\log (x)}}+x\right )}+\frac {\left (\frac {5}{e}\right )^{\frac {1}{\log \left (-e^{\frac {75+28 x+x \log (x)}{3+\log (x)}}+x\right )}} \left (-84+59 x-6 \log (x)+31 x \log (x)-\log ^2(x)+x \log ^2(x)\right )}{\left (-x+e^{\frac {75}{3+\log (x)}+\frac {28 x}{3+\log (x)}} x^{\frac {x}{3+\log (x)}}\right ) (3+\log (x))^2 \log ^2\left (-e^{\frac {75+28 x+x \log (x)}{3+\log (x)}}+x\right )}\right ) \, dx\\ &=(1-\log (5)) \int \frac {\left (\frac {5}{e}\right )^{\frac {1}{\log \left (-e^{\frac {75+28 x+x \log (x)}{3+\log (x)}}+x\right )}} \left (-75+59 x+31 x \log (x)+x \log ^2(x)\right )}{x (3+\log (x))^2 \log ^2\left (-e^{\frac {75+28 x+x \log (x)}{3+\log (x)}}+x\right )} \, dx+(1-\log (5)) \int \frac {\left (\frac {5}{e}\right )^{\frac {1}{\log \left (-e^{\frac {75+28 x+x \log (x)}{3+\log (x)}}+x\right )}} \left (-84+59 x-6 \log (x)+31 x \log (x)-\log ^2(x)+x \log ^2(x)\right )}{\left (-x+e^{\frac {75}{3+\log (x)}+\frac {28 x}{3+\log (x)}} x^{\frac {x}{3+\log (x)}}\right ) (3+\log (x))^2 \log ^2\left (-e^{\frac {75+28 x+x \log (x)}{3+\log (x)}}+x\right )} \, dx\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A]
time = 0.28, size = 31, normalized size = 1.07 \begin {gather*} \left (\frac {5}{e}\right )^{\frac {1}{\log \left (-e^{\frac {75+28 x+x \log (x)}{3+\log (x)}}+x\right )}} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.10, size = 31, normalized size = 1.07
method | result | size |
risch | \({\mathrm e}^{\frac {\ln \left (5\right )-1}{\ln \left (-{\mathrm e}^{\frac {x \ln \left (x \right )+28 x +75}{3+\ln \left (x \right )}}+x \right )}}\) | \(31\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [B] Leaf count of result is larger than twice the leaf count of optimal. 79 vs.
\(2 (27) = 54\).
time = 0.80, size = 79, normalized size = 2.72 \begin {gather*} e^{\left (\frac {\log \left (5\right )}{\log \left (x - e^{\left (\frac {x \log \left (x\right )}{\log \left (x\right ) + 3} + \frac {28 \, x}{\log \left (x\right ) + 3} + \frac {75}{\log \left (x\right ) + 3}\right )}\right )} - \frac {1}{\log \left (x - e^{\left (\frac {x \log \left (x\right )}{\log \left (x\right ) + 3} + \frac {28 \, x}{\log \left (x\right ) + 3} + \frac {75}{\log \left (x\right ) + 3}\right )}\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.33, size = 30, normalized size = 1.03 \begin {gather*} e^{\left (\frac {\log \left (5\right ) - 1}{\log \left (x - e^{\left (\frac {x \log \left (x\right ) + 28 \, x + 75}{\log \left (x\right ) + 3}\right )}\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [F(-1)] Timed out
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [F(-1)] Timed out
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 1.46, size = 78, normalized size = 2.69 \begin {gather*} 5^{\frac {1}{\ln \left (x-x^{\frac {x}{\ln \left (x\right )+3}}\,{\mathrm {e}}^{\frac {75}{\ln \left (x\right )+3}}\,{\mathrm {e}}^{\frac {28\,x}{\ln \left (x\right )+3}}\right )}}\,{\mathrm {e}}^{-\frac {1}{\ln \left (x-x^{\frac {x}{\ln \left (x\right )+3}}\,{\mathrm {e}}^{\frac {75}{\ln \left (x\right )+3}}\,{\mathrm {e}}^{\frac {28\,x}{\ln \left (x\right )+3}}\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________