Optimal. Leaf size=55 \[ -\frac {428}{243 (3 x+2)}+\frac {259}{81 (3 x+2)^2}-\frac {2009}{729 (3 x+2)^3}+\frac {343}{972 (3 x+2)^4}-\frac {40}{243} \log (3 x+2) \]
________________________________________________________________________________________
Rubi [A] time = 0.02, antiderivative size = 55, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.050, Rules used = {77} \begin {gather*} -\frac {428}{243 (3 x+2)}+\frac {259}{81 (3 x+2)^2}-\frac {2009}{729 (3 x+2)^3}+\frac {343}{972 (3 x+2)^4}-\frac {40}{243} \log (3 x+2) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 77
Rubi steps
\begin {align*} \int \frac {(1-2 x)^3 (3+5 x)}{(2+3 x)^5} \, dx &=\int \left (-\frac {343}{81 (2+3 x)^5}+\frac {2009}{81 (2+3 x)^4}-\frac {518}{27 (2+3 x)^3}+\frac {428}{81 (2+3 x)^2}-\frac {40}{81 (2+3 x)}\right ) \, dx\\ &=\frac {343}{972 (2+3 x)^4}-\frac {2009}{729 (2+3 x)^3}+\frac {259}{81 (2+3 x)^2}-\frac {428}{243 (2+3 x)}-\frac {40}{243} \log (2+3 x)\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.02, size = 41, normalized size = 0.75 \begin {gather*} -\frac {138672 x^3+193428 x^2+97116 x+480 (3 x+2)^4 \log (6 x+4)+18835}{2916 (3 x+2)^4} \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 (3+5 x)}{(2+3 x)^5} \, dx \end {gather*}
Verification is not applicable to the result.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 1.15, size = 67, normalized size = 1.22 \begin {gather*} -\frac {138672 \, x^{3} + 193428 \, x^{2} + 480 \, {\left (81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right )} \log \left (3 \, x + 2\right ) + 97116 \, x + 18835}{2916 \, {\left (81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 1.11, size = 55, normalized size = 1.00 \begin {gather*} -\frac {428}{243 \, {\left (3 \, x + 2\right )}} + \frac {259}{81 \, {\left (3 \, x + 2\right )}^{2}} - \frac {2009}{729 \, {\left (3 \, x + 2\right )}^{3}} + \frac {343}{972 \, {\left (3 \, x + 2\right )}^{4}} + \frac {40}{243} \, \log \left (\frac {{\left | 3 \, x + 2 \right |}}{3 \, {\left (3 \, x + 2\right )}^{2}}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.01, size = 46, normalized size = 0.84 \begin {gather*} -\frac {40 \ln \left (3 x +2\right )}{243}+\frac {343}{972 \left (3 x +2\right )^{4}}-\frac {2009}{729 \left (3 x +2\right )^{3}}+\frac {259}{81 \left (3 x +2\right )^{2}}-\frac {428}{243 \left (3 x +2\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.55, size = 48, normalized size = 0.87 \begin {gather*} -\frac {138672 \, x^{3} + 193428 \, x^{2} + 97116 \, x + 18835}{2916 \, {\left (81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right )}} - \frac {40}{243} \, \log \left (3 \, x + 2\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 1.09, size = 44, normalized size = 0.80 \begin {gather*} -\frac {40\,\ln \left (x+\frac {2}{3}\right )}{243}-\frac {\frac {428\,x^3}{729}+\frac {199\,x^2}{243}+\frac {8093\,x}{19683}+\frac {18835}{236196}}{x^4+\frac {8\,x^3}{3}+\frac {8\,x^2}{3}+\frac {32\,x}{27}+\frac {16}{81}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.15, size = 46, normalized size = 0.84 \begin {gather*} - \frac {138672 x^{3} + 193428 x^{2} + 97116 x + 18835}{236196 x^{4} + 629856 x^{3} + 629856 x^{2} + 279936 x + 46656} - \frac {40 \log {\left (3 x + 2 \right )}}{243} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________