Optimal. Leaf size=30 \[ \frac {4 x^3}{5}-\frac {28 x^2}{25}+\frac {43 x}{125}+\frac {121}{625} \log (5 x+3) \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.01, antiderivative size = 30, 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 = {77} \[ \frac {4 x^3}{5}-\frac {28 x^2}{25}+\frac {43 x}{125}+\frac {121}{625} \log (5 x+3) \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 77
Rubi steps
\begin {align*} \int \frac {(1-2 x)^2 (2+3 x)}{3+5 x} \, dx &=\int \left (\frac {43}{125}-\frac {56 x}{25}+\frac {12 x^2}{5}+\frac {121}{125 (3+5 x)}\right ) \, dx\\ &=\frac {43 x}{125}-\frac {28 x^2}{25}+\frac {4 x^3}{5}+\frac {121}{625} \log (3+5 x)\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.01, size = 27, normalized size = 0.90 \[ \frac {1}{625} \left (500 x^3-700 x^2+215 x+121 \log (5 x+3)+489\right ) \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.73, size = 22, normalized size = 0.73 \[ \frac {4}{5} \, x^{3} - \frac {28}{25} \, x^{2} + \frac {43}{125} \, x + \frac {121}{625} \, \log \left (5 \, x + 3\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 1.00, size = 23, normalized size = 0.77 \[ \frac {4}{5} \, x^{3} - \frac {28}{25} \, x^{2} + \frac {43}{125} \, x + \frac {121}{625} \, \log \left ({\left | 5 \, x + 3 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.00, size = 23, normalized size = 0.77 \[ \frac {4 x^{3}}{5}-\frac {28 x^{2}}{25}+\frac {43 x}{125}+\frac {121 \ln \left (5 x +3\right )}{625} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.52, size = 22, normalized size = 0.73 \[ \frac {4}{5} \, x^{3} - \frac {28}{25} \, x^{2} + \frac {43}{125} \, x + \frac {121}{625} \, \log \left (5 \, x + 3\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.03, size = 20, normalized size = 0.67 \[ \frac {43\,x}{125}+\frac {121\,\ln \left (x+\frac {3}{5}\right )}{625}-\frac {28\,x^2}{25}+\frac {4\,x^3}{5} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.09, size = 27, normalized size = 0.90 \[ \frac {4 x^{3}}{5} - \frac {28 x^{2}}{25} + \frac {43 x}{125} + \frac {121 \log {\left (5 x + 3 \right )}}{625} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________