Optimal. Leaf size=33 \[ \frac {44}{125 (5 x+3)}-\frac {121}{250 (5 x+3)^2}+\frac {4}{125} \log (5 x+3) \]
________________________________________________________________________________________
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} \begin {gather*} \frac {44}{125 (5 x+3)}-\frac {121}{250 (5 x+3)^2}+\frac {4}{125} \log (5 x+3) \end {gather*}
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 = 0.02, size = 31, normalized size = 0.94 \begin {gather*} \frac {440 x+8 (5 x+3)^2 \log (10 x+6)+143}{250 (5 x+3)^2} \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)^2}{(3+5 x)^3} \, dx \end {gather*}
Verification is not applicable to the result.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 1.20, size = 37, normalized size = 1.12 \begin {gather*} \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 {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.87, size = 24, normalized size = 0.73 \begin {gather*} \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 {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.00, size = 28, normalized size = 0.85 \begin {gather*} \frac {4 \ln \left (5 x +3\right )}{125}-\frac {121}{250 \left (5 x +3\right )^{2}}+\frac {44}{125 \left (5 x +3\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.46, size = 28, normalized size = 0.85 \begin {gather*} \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 {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.03, size = 23, normalized size = 0.70 \begin {gather*} \frac {4\,\ln \left (x+\frac {3}{5}\right )}{125}+\frac {\frac {44\,x}{625}+\frac {143}{6250}}{x^2+\frac {6\,x}{5}+\frac {9}{25}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.12, size = 24, normalized size = 0.73 \begin {gather*} \frac {440 x + 143}{6250 x^{2} + 7500 x + 2250} + \frac {4 \log {\left (5 x + 3 \right )}}{125} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________