Optimal. Leaf size=33 \[ \frac{44}{125 (5 x+3)}-\frac{121}{250 (5 x+3)^2}+\frac{4}{125} \log (5 x+3) \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.011919, antiderivative size = 33, 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} \[ \frac{44}{125 (5 x+3)}-\frac{121}{250 (5 x+3)^2}+\frac{4}{125} \log (5 x+3) \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 43
Rubi steps
\begin{align*} \int \frac{(1-2 x)^2}{(3+5 x)^3} \, dx &=\int \left (\frac{121}{25 (3+5 x)^3}-\frac{44}{25 (3+5 x)^2}+\frac{4}{25 (3+5 x)}\right ) \, dx\\ &=-\frac{121}{250 (3+5 x)^2}+\frac{44}{125 (3+5 x)}+\frac{4}{125} \log (3+5 x)\\ \end{align*}
Mathematica [A] time = 0.0112523, size = 31, normalized size = 0.94 \[ \frac{440 x+8 (5 x+3)^2 \log (10 x+6)+143}{250 (5 x+3)^2} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.005, size = 28, normalized size = 0.9 \begin{align*} -{\frac{121}{250\, \left ( 3+5\,x \right ) ^{2}}}+{\frac{44}{375+625\,x}}+{\frac{4\,\ln \left ( 3+5\,x \right ) }{125}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 1.1466, size = 38, normalized size = 1.15 \begin{align*} \frac{11 \,{\left (40 \, x + 13\right )}}{250 \,{\left (25 \, x^{2} + 30 \, x + 9\right )}} + \frac{4}{125} \, \log \left (5 \, x + 3\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.2269, size = 105, normalized size = 3.18 \begin{align*} \frac{8 \,{\left (25 \, x^{2} + 30 \, x + 9\right )} \log \left (5 \, x + 3\right ) + 440 \, x + 143}{250 \,{\left (25 \, x^{2} + 30 \, x + 9\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 0.107233, size = 24, normalized size = 0.73 \begin{align*} \frac{440 x + 143}{6250 x^{2} + 7500 x + 2250} + \frac{4 \log{\left (5 x + 3 \right )}}{125} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.45829, size = 32, normalized size = 0.97 \begin{align*} \frac{11 \,{\left (40 \, x + 13\right )}}{250 \,{\left (5 \, x + 3\right )}^{2}} + \frac{4}{125} \, \log \left ({\left | 5 \, x + 3 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]