Optimal. Leaf size=23 \[ \frac {4 e^5 \left (e^2+x-\log (5)+\log (2 x)\right )}{3 x} \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.02, antiderivative size = 41, normalized size of antiderivative = 1.78, number of steps
used = 2, number of rules used = 2, integrand size = 35, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.057, Rules used = {12, 2341}
\begin {gather*} \frac {4 e^5}{3 x}-\frac {4 \left (e^5 \left (1-e^2+\log (5)\right )-e^5 \log (2 x)\right )}{3 x} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 12
Rule 2341
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{3} \int \frac {e^5 \left (4-4 e^2\right )+4 e^5 \log (5)-4 e^5 \log (2 x)}{x^2} \, dx\\ &=\frac {4 e^5}{3 x}-\frac {4 \left (e^5 \left (1-e^2+\log (5)\right )-e^5 \log (2 x)\right )}{3 x}\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A]
time = 0.00, size = 27, normalized size = 1.17 \begin {gather*} \frac {4 e^7}{3 x}+\frac {4 e^5 \log \left (\frac {2 x}{5}\right )}{3 x} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [B] Leaf count of result is larger than twice the leaf count of optimal. \(47\) vs.
\(2(21)=42\).
time = 0.23, size = 48, normalized size = 2.09
method | result | size |
norman | \(\frac {\frac {4 \,{\mathrm e}^{5} \ln \left (2 x \right )}{3}+\frac {4 \,{\mathrm e}^{2} {\mathrm e}^{5}}{3}-\frac {4 \,{\mathrm e}^{5} \ln \left (5\right )}{3}}{x}\) | \(28\) |
risch | \(\frac {4 \,{\mathrm e}^{5} \ln \left (2 x \right )}{3 x}+\frac {4 \,{\mathrm e}^{5} {\mathrm e}^{2}}{3 x}-\frac {4 \,{\mathrm e}^{5} \ln \left (5\right )}{3 x}\) | \(31\) |
derivativedivides | \(\frac {4 \,{\mathrm e}^{5} {\mathrm e}^{2}}{3 x}-\frac {4 \,{\mathrm e}^{5} \ln \left (5\right )}{3 x}-\frac {8 \,{\mathrm e}^{5} \left (-\frac {\ln \left (2 x \right )}{2 x}-\frac {1}{2 x}\right )}{3}-\frac {4 \,{\mathrm e}^{5}}{3 x}\) | \(48\) |
default | \(\frac {4 \,{\mathrm e}^{5} {\mathrm e}^{2}}{3 x}-\frac {4 \,{\mathrm e}^{5} \ln \left (5\right )}{3 x}-\frac {8 \,{\mathrm e}^{5} \left (-\frac {\ln \left (2 x \right )}{2 x}-\frac {1}{2 x}\right )}{3}-\frac {4 \,{\mathrm e}^{5}}{3 x}\) | \(48\) |
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. 39 vs.
\(2 (19) = 38\).
time = 0.28, size = 39, normalized size = 1.70 \begin {gather*} -\frac {4 \, e^{5} \log \left (5\right )}{3 \, x} + \frac {4 \, {\left (e^{5} \log \left (2 \, x\right ) + e^{5}\right )}}{3 \, x} + \frac {4 \, e^{7}}{3 \, x} - \frac {4 \, e^{5}}{3 \, x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.38, size = 23, normalized size = 1.00 \begin {gather*} -\frac {4 \, {\left (e^{5} \log \left (5\right ) - e^{5} \log \left (2 \, x\right ) - e^{7}\right )}}{3 \, x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.06, size = 31, normalized size = 1.35 \begin {gather*} \frac {4 e^{5} \log {\left (2 x \right )}}{3 x} - \frac {- \frac {4 e^{7}}{3} + \frac {4 e^{5} \log {\left (5 \right )}}{3}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 0.41, size = 23, normalized size = 1.00 \begin {gather*} -\frac {4 \, {\left (e^{5} \log \left (5\right ) - e^{5} \log \left (2 \, x\right ) - e^{7}\right )}}{3 \, x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 4.45, size = 18, normalized size = 0.78 \begin {gather*} \frac {4\,{\mathrm {e}}^5\,\left (\ln \left (2\,x\right )+{\mathrm {e}}^2-\ln \left (5\right )\right )}{3\,x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________