Optimal. Leaf size=25 \[ 5-\frac {1}{x+\frac {(16+\log (x))^2}{e^{18} \left (3+e^3\right )}} \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.26, antiderivative size = 32, normalized size of antiderivative = 1.28, number of steps
used = 3, number of rules used = 3, integrand size = 159, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.019, Rules used = {6820, 12,
6818} \begin {gather*} -\frac {e^{18} \left (3+e^3\right )}{e^{18} \left (3+e^3\right ) x+\log ^2(x)+32 \log (x)+256} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 12
Rule 6818
Rule 6820
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {e^{18} \left (3+e^3\right ) \left (32+3 e^{18} \left (1+\frac {e^3}{3}\right ) x+2 \log (x)\right )}{x \left (256+3 e^{18} \left (1+\frac {e^3}{3}\right ) x+32 \log (x)+\log ^2(x)\right )^2} \, dx\\ &=\left (e^{18} \left (3+e^3\right )\right ) \int \frac {32+3 e^{18} \left (1+\frac {e^3}{3}\right ) x+2 \log (x)}{x \left (256+3 e^{18} \left (1+\frac {e^3}{3}\right ) x+32 \log (x)+\log ^2(x)\right )^2} \, dx\\ &=-\frac {e^{18} \left (3+e^3\right )}{256+e^{18} \left (3+e^3\right ) x+32 \log (x)+\log ^2(x)}\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A]
time = 0.02, size = 33, normalized size = 1.32 \begin {gather*} -\frac {e^{18} \left (3+e^3\right )}{256+\left (3 e^{18}+e^{21}\right ) x+32 \log (x)+\log ^2(x)} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 8.68, size = 33, normalized size = 1.32
method | result | size |
default | \(\frac {{\mathrm e}^{18} \left (-{\mathrm e}^{3}-3\right )}{{\mathrm e}^{3} {\mathrm e}^{18} x +3 \,{\mathrm e}^{18} x +\ln \left (x \right )^{2}+32 \ln \left (x \right )+256}\) | \(33\) |
norman | \(\frac {-{\mathrm e}^{18} {\mathrm e}^{3}-3 \,{\mathrm e}^{18}}{{\mathrm e}^{3} {\mathrm e}^{18} x +3 \,{\mathrm e}^{18} x +\ln \left (x \right )^{2}+32 \ln \left (x \right )+256}\) | \(36\) |
risch | \(-\frac {{\mathrm e}^{18} {\mathrm e}^{3}}{x \,{\mathrm e}^{21}+3 \,{\mathrm e}^{18} x +\ln \left (x \right )^{2}+32 \ln \left (x \right )+256}-\frac {3 \,{\mathrm e}^{18}}{x \,{\mathrm e}^{21}+3 \,{\mathrm e}^{18} x +\ln \left (x \right )^{2}+32 \ln \left (x \right )+256}\) | \(54\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.31, size = 30, normalized size = 1.20 \begin {gather*} -\frac {e^{21} + 3 \, e^{18}}{x {\left (e^{21} + 3 \, e^{18}\right )} + \log \left (x\right )^{2} + 32 \, \log \left (x\right ) + 256} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.38, size = 30, normalized size = 1.20 \begin {gather*} -\frac {e^{21} + 3 \, e^{18}}{x e^{21} + 3 \, x e^{18} + \log \left (x\right )^{2} + 32 \, \log \left (x\right ) + 256} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.09, size = 32, normalized size = 1.28 \begin {gather*} \frac {- e^{21} - 3 e^{18}}{3 x e^{18} + x e^{21} + \log {\left (x \right )}^{2} + 32 \log {\left (x \right )} + 256} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 0.66, size = 30, normalized size = 1.20 \begin {gather*} -\frac {2 \, {\left (e^{21} + 3 \, e^{18}\right )}}{x e^{21} + 3 \, x e^{18} + \log \left (x\right )^{2} + 32 \, \log \left (x\right ) + 256} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 10.87, size = 84, normalized size = 3.36 \begin {gather*} \frac {\frac {{\left (3\,{\mathrm {e}}^{18}+{\mathrm {e}}^{21}\right )}^2\,x^3}{256}+\left (\frac {3\,{\mathrm {e}}^{18}}{256}+\frac {{\mathrm {e}}^{21}}{256}\right )\,x^2\,{\ln \left (x\right )}^2+\left (\frac {3\,{\mathrm {e}}^{18}}{8}+\frac {{\mathrm {e}}^{21}}{8}\right )\,x^2\,\ln \left (x\right )}{32\,x^2\,\ln \left (x\right )+x^2\,{\ln \left (x\right )}^2+3\,x^3\,{\mathrm {e}}^{18}+x^3\,{\mathrm {e}}^{21}+256\,x^2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________