Optimal. Leaf size=43 \[ \frac {7}{44 (1-2 x)^2}+\frac {1}{121 (1-2 x)}-\frac {5 \log (1-2 x)}{1331}+\frac {5 \log (3+5 x)}{1331} \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.01, antiderivative size = 43, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 1, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.050, Rules used = {78}
\begin {gather*} \frac {1}{121 (1-2 x)}+\frac {7}{44 (1-2 x)^2}-\frac {5 \log (1-2 x)}{1331}+\frac {5 \log (5 x+3)}{1331} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 78
Rubi steps
\begin {align*} \int \frac {2+3 x}{(1-2 x)^3 (3+5 x)} \, dx &=\int \left (-\frac {7}{11 (-1+2 x)^3}+\frac {2}{121 (-1+2 x)^2}-\frac {10}{1331 (-1+2 x)}+\frac {25}{1331 (3+5 x)}\right ) \, dx\\ &=\frac {7}{44 (1-2 x)^2}+\frac {1}{121 (1-2 x)}-\frac {5 \log (1-2 x)}{1331}+\frac {5 \log (3+5 x)}{1331}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A]
time = 0.01, size = 46, normalized size = 1.07 \begin {gather*} \frac {891-88 x-20 (1-2 x)^2 \log (1-2 x)+20 (1-2 x)^2 \log (6+10 x)}{5324 (1-2 x)^2} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.09, size = 36, normalized size = 0.84
method | result | size |
risch | \(\frac {-\frac {2 x}{121}+\frac {81}{484}}{\left (-1+2 x \right )^{2}}-\frac {5 \ln \left (-1+2 x \right )}{1331}+\frac {5 \ln \left (3+5 x \right )}{1331}\) | \(32\) |
norman | \(\frac {\frac {79}{121} x -\frac {81}{121} x^{2}}{\left (-1+2 x \right )^{2}}-\frac {5 \ln \left (-1+2 x \right )}{1331}+\frac {5 \ln \left (3+5 x \right )}{1331}\) | \(35\) |
default | \(\frac {7}{44 \left (-1+2 x \right )^{2}}-\frac {1}{121 \left (-1+2 x \right )}-\frac {5 \ln \left (-1+2 x \right )}{1331}+\frac {5 \ln \left (3+5 x \right )}{1331}\) | \(36\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.38, size = 36, normalized size = 0.84 \begin {gather*} -\frac {8 \, x - 81}{484 \, {\left (4 \, x^{2} - 4 \, x + 1\right )}} + \frac {5}{1331} \, \log \left (5 \, x + 3\right ) - \frac {5}{1331} \, \log \left (2 \, x - 1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.43, size = 55, normalized size = 1.28 \begin {gather*} \frac {20 \, {\left (4 \, x^{2} - 4 \, x + 1\right )} \log \left (5 \, x + 3\right ) - 20 \, {\left (4 \, x^{2} - 4 \, x + 1\right )} \log \left (2 \, x - 1\right ) - 88 \, x + 891}{5324 \, {\left (4 \, x^{2} - 4 \, x + 1\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.05, size = 34, normalized size = 0.79 \begin {gather*} - \frac {8 x - 81}{1936 x^{2} - 1936 x + 484} - \frac {5 \log {\left (x - \frac {1}{2} \right )}}{1331} + \frac {5 \log {\left (x + \frac {3}{5} \right )}}{1331} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 1.45, size = 33, normalized size = 0.77 \begin {gather*} -\frac {8 \, x - 81}{484 \, {\left (2 \, x - 1\right )}^{2}} + \frac {5}{1331} \, \log \left ({\left | 5 \, x + 3 \right |}\right ) - \frac {5}{1331} \, \log \left ({\left | 2 \, x - 1 \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 0.04, size = 26, normalized size = 0.60 \begin {gather*} \frac {10\,\mathrm {atanh}\left (\frac {20\,x}{11}+\frac {1}{11}\right )}{1331}-\frac {\frac {x}{242}-\frac {81}{1936}}{x^2-x+\frac {1}{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________