Optimal. Leaf size=33 \[ -\frac {55}{4 (1-2 x)}+\frac {121}{16 (1-2 x)^2}-\frac {25}{8} \log (1-2 x) \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.01, antiderivative size = 33, normalized size of antiderivative = 1.00, 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} \[ -\frac {55}{4 (1-2 x)}+\frac {121}{16 (1-2 x)^2}-\frac {25}{8} \log (1-2 x) \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 43
Rubi steps
\begin {align*} \int \frac {(3+5 x)^2}{(1-2 x)^3} \, dx &=\int \left (-\frac {121}{4 (-1+2 x)^3}-\frac {55}{2 (-1+2 x)^2}-\frac {25}{4 (-1+2 x)}\right ) \, dx\\ &=\frac {121}{16 (1-2 x)^2}-\frac {55}{4 (1-2 x)}-\frac {25}{8} \log (1-2 x)\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.01, size = 33, normalized size = 1.00 \[ -\frac {55}{4 (1-2 x)}+\frac {121}{16 (1-2 x)^2}-\frac {25}{8} \log (1-2 x) \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.80, size = 37, normalized size = 1.12 \[ -\frac {50 \, {\left (4 \, x^{2} - 4 \, x + 1\right )} \log \left (2 \, x - 1\right ) - 440 \, x + 99}{16 \, {\left (4 \, x^{2} - 4 \, x + 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 1.17, size = 24, normalized size = 0.73 \[ \frac {11 \, {\left (40 \, x - 9\right )}}{16 \, {\left (2 \, x - 1\right )}^{2}} - \frac {25}{8} \, \log \left ({\left | 2 \, x - 1 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.01, size = 28, normalized size = 0.85 \[ -\frac {25 \ln \left (2 x -1\right )}{8}+\frac {121}{16 \left (2 x -1\right )^{2}}+\frac {55}{4 \left (2 x -1\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.71, size = 28, normalized size = 0.85 \[ \frac {11 \, {\left (40 \, x - 9\right )}}{16 \, {\left (4 \, x^{2} - 4 \, x + 1\right )}} - \frac {25}{8} \, \log \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.03, size = 23, normalized size = 0.70 \[ \frac {\frac {55\,x}{8}-\frac {99}{64}}{x^2-x+\frac {1}{4}}-\frac {25\,\ln \left (x-\frac {1}{2}\right )}{8} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.12, size = 26, normalized size = 0.79 \[ - \frac {99 - 440 x}{64 x^{2} - 64 x + 16} - \frac {25 \log {\left (2 x - 1 \right )}}{8} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________