Optimal. Leaf size=22 \[ -\frac {11}{25 (5 x+3)}-\frac {2}{25} \log (5 x+3) \]
________________________________________________________________________________________
Rubi [A] time = 0.01, antiderivative size = 22, normalized size of antiderivative = 1.00, 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} \begin {gather*} -\frac {11}{25 (5 x+3)}-\frac {2}{25} \log (5 x+3) \end {gather*}
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 = 0.00, size = 22, normalized size = 1.00 \begin {gather*} -\frac {11}{25 (5 x+3)}-\frac {2}{25} \log (5 x+3) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {1-2 x}{(3+5 x)^2} \, dx \end {gather*}
Verification is not applicable to the result.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 1.24, size = 24, normalized size = 1.09 \begin {gather*} -\frac {2 \, {\left (5 \, x + 3\right )} \log \left (5 \, x + 3\right ) + 11}{25 \, {\left (5 \, x + 3\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 1.17, size = 28, normalized size = 1.27 \begin {gather*} -\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 {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.01, size = 19, normalized size = 0.86 \begin {gather*} -\frac {2 \ln \left (5 x +3\right )}{25}-\frac {11}{25 \left (5 x +3\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.58, size = 18, normalized size = 0.82 \begin {gather*} -\frac {11}{25 \, {\left (5 \, x + 3\right )}} - \frac {2}{25} \, \log \left (5 \, x + 3\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.03, size = 16, normalized size = 0.73 \begin {gather*} -\frac {2\,\ln \left (x+\frac {3}{5}\right )}{25}-\frac {11}{125\,\left (x+\frac {3}{5}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.09, size = 17, normalized size = 0.77 \begin {gather*} - \frac {2 \log {\left (5 x + 3 \right )}}{25} - \frac {11}{125 x + 75} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________