Optimal. Leaf size=18 \[ \frac {3 e^{11/4} (x+\log (2 x))}{2 x^2} \]
[Out]
________________________________________________________________________________________
Rubi [B] Leaf count is larger than twice the leaf count of optimal. \(48\) vs. \(2(18)=36\).
time = 0.02, antiderivative size = 48, normalized size of antiderivative = 2.67, number of steps
used = 5, number of rules used = 4, integrand size = 30, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.133, Rules used = {12, 14, 37,
2341} \begin {gather*} -\frac {3 e^{11/4} (1-x)^2}{4 x^2}+\frac {3 e^{11/4}}{4 x^2}+\frac {3 e^{11/4} \log (2 x)}{2 x^2} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 12
Rule 14
Rule 37
Rule 2341
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{2} \int \frac {e^{11/4} (3-3 x)-6 e^{11/4} \log (2 x)}{x^3} \, dx\\ &=\frac {1}{2} \int \left (-\frac {3 e^{11/4} (-1+x)}{x^3}-\frac {6 e^{11/4} \log (2 x)}{x^3}\right ) \, dx\\ &=-\left (\frac {1}{2} \left (3 e^{11/4}\right ) \int \frac {-1+x}{x^3} \, dx\right )-\left (3 e^{11/4}\right ) \int \frac {\log (2 x)}{x^3} \, dx\\ &=\frac {3 e^{11/4}}{4 x^2}-\frac {3 e^{11/4} (1-x)^2}{4 x^2}+\frac {3 e^{11/4} \log (2 x)}{2 x^2}\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A]
time = 0.01, size = 24, normalized size = 1.33 \begin {gather*} -\frac {3}{2} e^{11/4} \left (-\frac {1}{x}-\frac {\log (2 x)}{x^2}\right ) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [B] Leaf count of result is larger than twice the leaf count of optimal. \(34\) vs.
\(2(13)=26\).
time = 0.35, size = 35, normalized size = 1.94
method | result | size |
norman | \(\frac {\frac {3 \,{\mathrm e}^{\frac {11}{4}} x}{2}+\frac {3 \,{\mathrm e}^{\frac {11}{4}} \ln \left (2 x \right )}{2}}{x^{2}}\) | \(19\) |
risch | \(\frac {3 \,{\mathrm e}^{\frac {11}{4}} \ln \left (2 x \right )}{2 x^{2}}+\frac {3 \,{\mathrm e}^{\frac {11}{4}}}{2 x}\) | \(20\) |
derivativedivides | \(-12 \,{\mathrm e}^{\frac {11}{4}} \left (-\frac {\ln \left (2 x \right )}{8 x^{2}}-\frac {1}{16 x^{2}}\right )+\frac {3 \,{\mathrm e}^{\frac {11}{4}}}{2 x}-\frac {3 \,{\mathrm e}^{\frac {11}{4}}}{4 x^{2}}\) | \(35\) |
default | \(-12 \,{\mathrm e}^{\frac {11}{4}} \left (-\frac {\ln \left (2 x \right )}{8 x^{2}}-\frac {1}{16 x^{2}}\right )+\frac {3 \,{\mathrm e}^{\frac {11}{4}}}{2 x}-\frac {3 \,{\mathrm e}^{\frac {11}{4}}}{4 x^{2}}\) | \(35\) |
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. 32 vs.
\(2 (13) = 26\).
time = 0.30, size = 32, normalized size = 1.78 \begin {gather*} \frac {3}{4} \, {\left (\frac {2 \, \log \left (2 \, x\right )}{x^{2}} + \frac {1}{x^{2}}\right )} e^{\frac {11}{4}} + \frac {3 \, e^{\frac {11}{4}}}{2 \, x} - \frac {3 \, e^{\frac {11}{4}}}{4 \, x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.42, size = 17, normalized size = 0.94 \begin {gather*} \frac {3 \, {\left (x e^{\frac {11}{4}} + e^{\frac {11}{4}} \log \left (2 \, x\right )\right )}}{2 \, x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.05, size = 26, normalized size = 1.44 \begin {gather*} \frac {3 e^{\frac {11}{4}}}{2 x} + \frac {3 e^{\frac {11}{4}} \log {\left (2 x \right )}}{2 x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 0.41, size = 17, normalized size = 0.94 \begin {gather*} \frac {3 \, {\left (x e^{\frac {11}{4}} + e^{\frac {11}{4}} \log \left (2 \, x\right )\right )}}{2 \, x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 4.22, size = 13, normalized size = 0.72 \begin {gather*} \frac {3\,{\mathrm {e}}^{11/4}\,\left (x+\ln \left (2\,x\right )\right )}{2\,x^2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________