Optimal. Leaf size=16 \[ \frac{11}{25} \log (5 x+3)-\frac{2 x}{5} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0071116, antiderivative size = 16, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.077, Rules used = {43} \[ \frac{11}{25} \log (5 x+3)-\frac{2 x}{5} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 43
Rubi steps
\begin{align*} \int \frac{1-2 x}{3+5 x} \, dx &=\int \left (-\frac{2}{5}+\frac{11}{5 (3+5 x)}\right ) \, dx\\ &=-\frac{2 x}{5}+\frac{11}{25} \log (3+5 x)\\ \end{align*}
Mathematica [A] time = 0.0027299, size = 17, normalized size = 1.06 \[ \frac{1}{25} (-10 x+11 \log (5 x+3)-6) \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.003, size = 13, normalized size = 0.8 \begin{align*} -{\frac{2\,x}{5}}+{\frac{11\,\ln \left ( 3+5\,x \right ) }{25}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 1.25247, size = 16, normalized size = 1. \begin{align*} -\frac{2}{5} \, x + \frac{11}{25} \, \log \left (5 \, x + 3\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.46048, size = 39, normalized size = 2.44 \begin{align*} -\frac{2}{5} \, x + \frac{11}{25} \, \log \left (5 \, x + 3\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 0.07203, size = 14, normalized size = 0.88 \begin{align*} - \frac{2 x}{5} + \frac{11 \log{\left (5 x + 3 \right )}}{25} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 2.86108, size = 18, normalized size = 1.12 \begin{align*} -\frac{2}{5} \, x + \frac{11}{25} \, \log \left ({\left | 5 \, x + 3 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]