Optimal. Leaf size=23 \[ \frac {25 \log ^2\left (4 e^{2 x} x^2 (\log (2)+\log (x))\right )}{x^2} \]
[Out]
________________________________________________________________________________________
Rubi [F]
time = 2.21, 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 {(50+(100+100 x) \log (2)+(100+100 x) \log (x)) \log \left (4 e^{2 x} x^2 \log (2)+4 e^{2 x} x^2 \log (x)\right )+(-50 \log (2)-50 \log (x)) \log ^2\left (4 e^{2 x} x^2 \log (2)+4 e^{2 x} x^2 \log (x)\right )}{x^3 \log (2)+x^3 \log (x)} \, dx \end {gather*}
Verification is not applicable to the result.
[In]
[Out]
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {(50+(100+100 x) \log (2)+(100+100 x) \log (x)) \log \left (4 e^{2 x} x^2 \log (2)+4 e^{2 x} x^2 \log (x)\right )+(-50 \log (2)-50 \log (x)) \log ^2\left (4 e^{2 x} x^2 \log (2)+4 e^{2 x} x^2 \log (x)\right )}{x^3 (\log (2)+\log (x))} \, dx\\ &=\int \frac {50 \log \left (4 e^{2 x} x^2 \log (2 x)\right ) \left (1+\log (4)+x \log (4)+2 (1+x) \log (x)-\log (2 x) \log \left (4 e^{2 x} x^2 \log (2 x)\right )\right )}{x^3 \log (2 x)} \, dx\\ &=50 \int \frac {\log \left (4 e^{2 x} x^2 \log (2 x)\right ) \left (1+\log (4)+x \log (4)+2 (1+x) \log (x)-\log (2 x) \log \left (4 e^{2 x} x^2 \log (2 x)\right )\right )}{x^3 \log (2 x)} \, dx\\ &=50 \int \left (\frac {(1+\log (4)+x \log (4)+2 \log (x)+2 x \log (x)) \log \left (4 e^{2 x} x^2 \log (2 x)\right )}{x^3 \log (2 x)}-\frac {\log ^2\left (4 e^{2 x} x^2 \log (2 x)\right )}{x^3}\right ) \, dx\\ &=50 \int \frac {(1+\log (4)+x \log (4)+2 \log (x)+2 x \log (x)) \log \left (4 e^{2 x} x^2 \log (2 x)\right )}{x^3 \log (2 x)} \, dx-50 \int \frac {\log ^2\left (4 e^{2 x} x^2 \log (2 x)\right )}{x^3} \, dx\\ &=-\left (50 \int \frac {\log ^2\left (4 e^{2 x} x^2 \log (2 x)\right )}{x^3} \, dx\right )+50 \int \left (\frac {\log (4) \log \left (4 e^{2 x} x^2 \log (2 x)\right )}{x^2 \log (2 x)}+\frac {(1+\log (4)) \log \left (4 e^{2 x} x^2 \log (2 x)\right )}{x^3 \log (2 x)}+\frac {2 \log (x) \log \left (4 e^{2 x} x^2 \log (2 x)\right )}{x^3 \log (2 x)}+\frac {2 \log (x) \log \left (4 e^{2 x} x^2 \log (2 x)\right )}{x^2 \log (2 x)}\right ) \, dx\\ &=-\left (50 \int \frac {\log ^2\left (4 e^{2 x} x^2 \log (2 x)\right )}{x^3} \, dx\right )+100 \int \frac {\log (x) \log \left (4 e^{2 x} x^2 \log (2 x)\right )}{x^3 \log (2 x)} \, dx+100 \int \frac {\log (x) \log \left (4 e^{2 x} x^2 \log (2 x)\right )}{x^2 \log (2 x)} \, dx+(50 \log (4)) \int \frac {\log \left (4 e^{2 x} x^2 \log (2 x)\right )}{x^2 \log (2 x)} \, dx+(50 (1+\log (4))) \int \frac {\log \left (4 e^{2 x} x^2 \log (2 x)\right )}{x^3 \log (2 x)} \, dx\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [F]
time = 0.30, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {(50+(100+100 x) \log (2)+(100+100 x) \log (x)) \log \left (4 e^{2 x} x^2 \log (2)+4 e^{2 x} x^2 \log (x)\right )+(-50 \log (2)-50 \log (x)) \log ^2\left (4 e^{2 x} x^2 \log (2)+4 e^{2 x} x^2 \log (x)\right )}{x^3 \log (2)+x^3 \log (x)} \, dx \end {gather*}
Verification is not applicable to the result.
[In]
[Out]
________________________________________________________________________________________
Maple [C] Result contains higher order function than in optimal. Order 9 vs. order
3.
time = 0.76, size = 5485, normalized size = 238.48
method | result | size |
risch | \(\text {Expression too large to display}\) | \(5485\) |
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. 53 vs.
\(2 (22) = 44\).
time = 0.52, size = 53, normalized size = 2.30 \begin {gather*} \frac {25 \, {\left (8 \, x \log \left (2\right ) + 4 \, \log \left (2\right )^{2} + 8 \, {\left (x + \log \left (2\right )\right )} \log \left (x\right ) + 4 \, \log \left (x\right )^{2} + 4 \, {\left (x + \log \left (2\right ) + \log \left (x\right )\right )} \log \left (\log \left (2\right ) + \log \left (x\right )\right ) + \log \left (\log \left (2\right ) + \log \left (x\right )\right )^{2}\right )}}{x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.39, size = 31, normalized size = 1.35 \begin {gather*} \frac {25 \, \log \left (4 \, x^{2} e^{\left (2 \, x\right )} \log \left (2\right ) + 4 \, x^{2} e^{\left (2 \, x\right )} \log \left (x\right )\right )^{2}}{x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.27, size = 34, normalized size = 1.48 \begin {gather*} \frac {25 \log {\left (4 x^{2} e^{2 x} \log {\left (x \right )} + 4 x^{2} e^{2 x} \log {\left (2 \right )} \right )}^{2}}{x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [B] Leaf count of result is larger than twice the leaf count of optimal. 72 vs.
\(2 (22) = 44\).
time = 0.50, size = 72, normalized size = 3.13 \begin {gather*} 100 \, {\left (\frac {x + \log \left (2\right )}{x^{2}} + \frac {\log \left (x\right )}{x^{2}}\right )} \log \left (\log \left (2\right ) + \log \left (x\right )\right ) + \frac {200 \, {\left (x + \log \left (2\right )\right )} \log \left (x\right )}{x^{2}} + \frac {100 \, \log \left (x\right )^{2}}{x^{2}} + \frac {25 \, \log \left (\log \left (2\right ) + \log \left (x\right )\right )^{2}}{x^{2}} + \frac {100 \, {\left (2 \, x \log \left (2\right ) + \log \left (2\right )^{2}\right )}}{x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [F]
time = 0.00, size = -1, normalized size = -0.04 \begin {gather*} \int -\frac {{\ln \left (4\,x^2\,{\mathrm {e}}^{2\,x}\,\ln \left (x\right )+4\,x^2\,{\mathrm {e}}^{2\,x}\,\ln \left (2\right )\right )}^2\,\left (50\,\ln \left (2\right )+50\,\ln \left (x\right )\right )-\ln \left (4\,x^2\,{\mathrm {e}}^{2\,x}\,\ln \left (x\right )+4\,x^2\,{\mathrm {e}}^{2\,x}\,\ln \left (2\right )\right )\,\left (\ln \left (2\right )\,\left (100\,x+100\right )+\ln \left (x\right )\,\left (100\,x+100\right )+50\right )}{x^3\,\ln \left (x\right )+x^3\,\ln \left (2\right )} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________