Optimal. Leaf size=22 \[ -\frac{11}{25 (5 x+3)}-\frac{2}{25} \log (5 x+3) \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0080255, antiderivative size = 22, 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} \[ -\frac{11}{25 (5 x+3)}-\frac{2}{25} \log (5 x+3) \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 43
Rubi steps
\begin{align*} \int \frac{1-2 x}{(3+5 x)^2} \, dx &=\int \left (\frac{11}{5 (3+5 x)^2}-\frac{2}{5 (3+5 x)}\right ) \, dx\\ &=-\frac{11}{25 (3+5 x)}-\frac{2}{25} \log (3+5 x)\\ \end{align*}
Mathematica [A] time = 0.0041088, size = 22, normalized size = 1. \[ -\frac{11}{25 (5 x+3)}-\frac{2}{25} \log (5 x+3) \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.005, size = 19, normalized size = 0.9 \begin{align*} -{\frac{11}{75+125\,x}}-{\frac{2\,\ln \left ( 3+5\,x \right ) }{25}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 1.03629, size = 24, normalized size = 1.09 \begin{align*} -\frac{11}{25 \,{\left (5 \, x + 3\right )}} - \frac{2}{25} \, \log \left (5 \, x + 3\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.43811, size = 66, normalized size = 3. \begin{align*} -\frac{2 \,{\left (5 \, x + 3\right )} \log \left (5 \, x + 3\right ) + 11}{25 \,{\left (5 \, x + 3\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 0.086074, size = 17, normalized size = 0.77 \begin{align*} - \frac{2 \log{\left (5 x + 3 \right )}}{25} - \frac{11}{125 x + 75} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 2.64249, size = 38, normalized size = 1.73 \begin{align*} -\frac{11}{25 \,{\left (5 \, x + 3\right )}} + \frac{2}{25} \, \log \left (\frac{{\left | 5 \, x + 3 \right |}}{5 \,{\left (5 \, x + 3\right )}^{2}}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]