Optimal. Leaf size=37 \[ -\frac {27 x}{50}-\frac {1}{1375 (3+5 x)}-\frac {343}{484} \log (1-2 x)+\frac {101 \log (3+5 x)}{15125} \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.01, antiderivative size = 37, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 1, integrand size = 22, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.045, Rules used = {90}
\begin {gather*} -\frac {27 x}{50}-\frac {1}{1375 (5 x+3)}-\frac {343}{484} \log (1-2 x)+\frac {101 \log (5 x+3)}{15125} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 90
Rubi steps
\begin {align*} \int \frac {(2+3 x)^3}{(1-2 x) (3+5 x)^2} \, dx &=\int \left (-\frac {27}{50}-\frac {343}{242 (-1+2 x)}+\frac {1}{275 (3+5 x)^2}+\frac {101}{3025 (3+5 x)}\right ) \, dx\\ &=-\frac {27 x}{50}-\frac {1}{1375 (3+5 x)}-\frac {343}{484} \log (1-2 x)+\frac {101 \log (3+5 x)}{15125}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A]
time = 0.02, size = 37, normalized size = 1.00 \begin {gather*} \frac {16335 (1-2 x)-\frac {44}{3+5 x}-42875 \log (1-2 x)+404 \log (6+10 x)}{60500} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.11, size = 30, normalized size = 0.81
method | result | size |
risch | \(-\frac {27 x}{50}-\frac {1}{6875 \left (x +\frac {3}{5}\right )}-\frac {343 \ln \left (-1+2 x \right )}{484}+\frac {101 \ln \left (3+5 x \right )}{15125}\) | \(28\) |
default | \(-\frac {27 x}{50}-\frac {343 \ln \left (-1+2 x \right )}{484}-\frac {1}{1375 \left (3+5 x \right )}+\frac {101 \ln \left (3+5 x \right )}{15125}\) | \(30\) |
norman | \(\frac {-\frac {2671}{1650} x -\frac {27}{10} x^{2}}{3+5 x}-\frac {343 \ln \left (-1+2 x \right )}{484}+\frac {101 \ln \left (3+5 x \right )}{15125}\) | \(35\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.31, size = 29, normalized size = 0.78 \begin {gather*} -\frac {27}{50} \, x - \frac {1}{1375 \, {\left (5 \, x + 3\right )}} + \frac {101}{15125} \, \log \left (5 \, x + 3\right ) - \frac {343}{484} \, \log \left (2 \, x - 1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.83, size = 45, normalized size = 1.22 \begin {gather*} -\frac {163350 \, x^{2} - 404 \, {\left (5 \, x + 3\right )} \log \left (5 \, x + 3\right ) + 42875 \, {\left (5 \, x + 3\right )} \log \left (2 \, x - 1\right ) + 98010 \, x + 44}{60500 \, {\left (5 \, x + 3\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.06, size = 31, normalized size = 0.84 \begin {gather*} - \frac {27 x}{50} - \frac {343 \log {\left (x - \frac {1}{2} \right )}}{484} + \frac {101 \log {\left (x + \frac {3}{5} \right )}}{15125} - \frac {1}{6875 x + 4125} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 0.89, size = 47, normalized size = 1.27 \begin {gather*} -\frac {27}{50} \, x - \frac {1}{1375 \, {\left (5 \, x + 3\right )}} + \frac {351}{500} \, \log \left (\frac {{\left | 5 \, x + 3 \right |}}{5 \, {\left (5 \, x + 3\right )}^{2}}\right ) - \frac {343}{484} \, \log \left ({\left | -\frac {11}{5 \, x + 3} + 2 \right |}\right ) - \frac {81}{250} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 1.12, size = 25, normalized size = 0.68 \begin {gather*} \frac {101\,\ln \left (x+\frac {3}{5}\right )}{15125}-\frac {343\,\ln \left (x-\frac {1}{2}\right )}{484}-\frac {27\,x}{50}-\frac {1}{6875\,\left (x+\frac {3}{5}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________