Optimal. Leaf size=30 \[ -\frac{8 x^3}{15}+\frac{42 x^2}{25}-\frac{402 x}{125}+\frac{1331}{625} \log (5 x+3) \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0100767, antiderivative size = 30, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.067, Rules used = {43} \[ -\frac{8 x^3}{15}+\frac{42 x^2}{25}-\frac{402 x}{125}+\frac{1331}{625} \log (5 x+3) \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 43
Rubi steps
\begin{align*} \int \frac{(1-2 x)^3}{3+5 x} \, dx &=\int \left (-\frac{402}{125}+\frac{84 x}{25}-\frac{8 x^2}{5}+\frac{1331}{125 (3+5 x)}\right ) \, dx\\ &=-\frac{402 x}{125}+\frac{42 x^2}{25}-\frac{8 x^3}{15}+\frac{1331}{625} \log (3+5 x)\\ \end{align*}
Mathematica [A] time = 0.0070239, size = 27, normalized size = 0.9 \[ \frac{-1000 x^3+3150 x^2-6030 x+3993 \log (5 x+3)-4968}{1875} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.001, size = 23, normalized size = 0.8 \begin{align*} -{\frac{402\,x}{125}}+{\frac{42\,{x}^{2}}{25}}-{\frac{8\,{x}^{3}}{15}}+{\frac{1331\,\ln \left ( 3+5\,x \right ) }{625}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 1.08798, size = 30, normalized size = 1. \begin{align*} -\frac{8}{15} \, x^{3} + \frac{42}{25} \, x^{2} - \frac{402}{125} \, x + \frac{1331}{625} \, \log \left (5 \, x + 3\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.53921, size = 80, normalized size = 2.67 \begin{align*} -\frac{8}{15} \, x^{3} + \frac{42}{25} \, x^{2} - \frac{402}{125} \, x + \frac{1331}{625} \, \log \left (5 \, x + 3\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 0.080046, size = 27, normalized size = 0.9 \begin{align*} - \frac{8 x^{3}}{15} + \frac{42 x^{2}}{25} - \frac{402 x}{125} + \frac{1331 \log{\left (5 x + 3 \right )}}{625} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 2.80305, size = 31, normalized size = 1.03 \begin{align*} -\frac{8}{15} \, x^{3} + \frac{42}{25} \, x^{2} - \frac{402}{125} \, x + \frac{1331}{625} \, \log \left ({\left | 5 \, x + 3 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]