Optimal. Leaf size=23 \[ \frac{2 x^2}{5}-\frac{32 x}{25}+\frac{121}{125} \log (5 x+3) \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0078704, antiderivative size = 23, 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} \[ \frac{2 x^2}{5}-\frac{32 x}{25}+\frac{121}{125} \log (5 x+3) \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 43
Rubi steps
\begin{align*} \int \frac{(1-2 x)^2}{3+5 x} \, dx &=\int \left (-\frac{32}{25}+\frac{4 x}{5}+\frac{121}{25 (3+5 x)}\right ) \, dx\\ &=-\frac{32 x}{25}+\frac{2 x^2}{5}+\frac{121}{125} \log (3+5 x)\\ \end{align*}
Mathematica [A] time = 0.0055031, size = 22, normalized size = 0.96 \[ \frac{1}{125} \left (50 x^2-160 x+121 \log (5 x+3)-114\right ) \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.003, size = 18, normalized size = 0.8 \begin{align*} -{\frac{32\,x}{25}}+{\frac{2\,{x}^{2}}{5}}+{\frac{121\,\ln \left ( 3+5\,x \right ) }{125}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 1.02713, size = 23, normalized size = 1. \begin{align*} \frac{2}{5} \, x^{2} - \frac{32}{25} \, x + \frac{121}{125} \, \log \left (5 \, x + 3\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.56635, size = 57, normalized size = 2.48 \begin{align*} \frac{2}{5} \, x^{2} - \frac{32}{25} \, x + \frac{121}{125} \, \log \left (5 \, x + 3\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 0.076658, size = 20, normalized size = 0.87 \begin{align*} \frac{2 x^{2}}{5} - \frac{32 x}{25} + \frac{121 \log{\left (5 x + 3 \right )}}{125} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 2.24137, size = 24, normalized size = 1.04 \begin{align*} \frac{2}{5} \, x^{2} - \frac{32}{25} \, x + \frac{121}{125} \, \log \left ({\left | 5 \, x + 3 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]