Optimal. Leaf size=20 \[ \frac {3}{10 x \log \left (\frac {e^x}{27 x^2}\right )} \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.08, antiderivative size = 20, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 2, integrand size = 38, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.053, Rules used = {12, 6819}
\begin {gather*} \frac {3}{10 x \log \left (\frac {e^x}{27 x^2}\right )} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 12
Rule 6819
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{10} \int \frac {6-3 x-3 \log \left (\frac {e^x}{27 x^2}\right )}{x^2 \log ^2\left (\frac {e^x}{27 x^2}\right )} \, dx\\ &=\frac {3}{10 x \log \left (\frac {e^x}{27 x^2}\right )}\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A]
time = 1.17, size = 20, normalized size = 1.00 \begin {gather*} \frac {3}{10 x \log \left (\frac {e^x}{27 x^2}\right )} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 14.85, size = 16, normalized size = 0.80
method | result | size |
default | \(\frac {3}{10 x \ln \left (\frac {{\mathrm e}^{x}}{27 x^{2}}\right )}\) | \(16\) |
norman | \(\frac {3}{10 x \ln \left (\frac {{\mathrm e}^{x}}{27 x^{2}}\right )}\) | \(16\) |
risch | \(-\frac {3}{5 x \left (6 \ln \left (3\right )+4 \ln \left (x \right )-2 \ln \left ({\mathrm e}^{x}\right )-i \pi \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i x^{2}\right )+2 i \pi \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )^{2}-i \pi \mathrm {csgn}\left (i x^{2}\right )^{3}-i \pi \mathrm {csgn}\left (\frac {i {\mathrm e}^{x}}{x^{2}}\right )^{2} \mathrm {csgn}\left (\frac {i}{x^{2}}\right )-i \pi \mathrm {csgn}\left (\frac {i {\mathrm e}^{x}}{x^{2}}\right )^{2} \mathrm {csgn}\left (i {\mathrm e}^{x}\right )+i \pi \,\mathrm {csgn}\left (\frac {i {\mathrm e}^{x}}{x^{2}}\right ) \mathrm {csgn}\left (\frac {i}{x^{2}}\right ) \mathrm {csgn}\left (i {\mathrm e}^{x}\right )+i \pi \mathrm {csgn}\left (\frac {i {\mathrm e}^{x}}{x^{2}}\right )^{3}\right )}\) | \(155\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.54, size = 18, normalized size = 0.90 \begin {gather*} \frac {3}{10 \, {\left (x^{2} - 3 \, x \log \left (3\right ) - 2 \, x \log \left (x\right )\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.38, size = 15, normalized size = 0.75 \begin {gather*} \frac {3}{10 \, x \log \left (\frac {e^{x}}{27 \, x^{2}}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.05, size = 14, normalized size = 0.70 \begin {gather*} \frac {3}{10 x \log {\left (\frac {e^{x}}{27 x^{2}} \right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 0.46, size = 17, normalized size = 0.85 \begin {gather*} \frac {3}{10 \, {\left (x^{2} - x \log \left (27 \, x^{2}\right )\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 3.25, size = 15, normalized size = 0.75 \begin {gather*} \frac {3}{10\,x\,\left (x+\ln \left (\frac {1}{27\,x^2}\right )\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________