Optimal. Leaf size=23 \[ \frac {13 x}{25}-\frac {3 x^2}{5}+\frac {11}{125} \log (3+5 x) \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.01, antiderivative size = 23, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 1, integrand size = 18, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.056, Rules used = {78}
\begin {gather*} -\frac {3 x^2}{5}+\frac {13 x}{25}+\frac {11}{125} \log (5 x+3) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 78
Rubi steps
\begin {align*} \int \frac {(1-2 x) (2+3 x)}{3+5 x} \, dx &=\int \left (\frac {13}{25}-\frac {6 x}{5}+\frac {11}{25 (3+5 x)}\right ) \, dx\\ &=\frac {13 x}{25}-\frac {3 x^2}{5}+\frac {11}{125} \log (3+5 x)\\ \end {align*}
________________________________________________________________________________________
Mathematica [A]
time = 0.00, size = 22, normalized size = 0.96 \begin {gather*} \frac {1}{125} \left (66+65 x-75 x^2+11 \log (3+5 x)\right ) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.10, size = 18, normalized size = 0.78
method | result | size |
default | \(\frac {13 x}{25}-\frac {3 x^{2}}{5}+\frac {11 \ln \left (3+5 x \right )}{125}\) | \(18\) |
norman | \(\frac {13 x}{25}-\frac {3 x^{2}}{5}+\frac {11 \ln \left (3+5 x \right )}{125}\) | \(18\) |
risch | \(\frac {13 x}{25}-\frac {3 x^{2}}{5}+\frac {11 \ln \left (3+5 x \right )}{125}\) | \(18\) |
meijerg | \(\frac {11 \ln \left (1+\frac {5 x}{3}\right )}{125}-\frac {x}{5}+\frac {3 x \left (-5 x +6\right )}{25}\) | \(21\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.32, size = 17, normalized size = 0.74 \begin {gather*} -\frac {3}{5} \, x^{2} + \frac {13}{25} \, x + \frac {11}{125} \, \log \left (5 \, x + 3\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.91, size = 17, normalized size = 0.74 \begin {gather*} -\frac {3}{5} \, x^{2} + \frac {13}{25} \, x + \frac {11}{125} \, \log \left (5 \, x + 3\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.02, size = 20, normalized size = 0.87 \begin {gather*} - \frac {3 x^{2}}{5} + \frac {13 x}{25} + \frac {11 \log {\left (5 x + 3 \right )}}{125} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 1.32, size = 18, normalized size = 0.78 \begin {gather*} -\frac {3}{5} \, x^{2} + \frac {13}{25} \, x + \frac {11}{125} \, \log \left ({\left | 5 \, x + 3 \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 0.03, size = 15, normalized size = 0.65 \begin {gather*} \frac {13\,x}{25}+\frac {11\,\ln \left (x+\frac {3}{5}\right )}{125}-\frac {3\,x^2}{5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________