Optimal. Leaf size=49 \[ \frac {100 x}{81}-\frac {503}{81 (3 x+2)}+\frac {259}{243 (3 x+2)^2}-\frac {49}{729 (3 x+2)^3}-\frac {740}{243} \log (3 x+2) \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.02, antiderivative size = 49, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 22, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.045, Rules used = {88} \[ \frac {100 x}{81}-\frac {503}{81 (3 x+2)}+\frac {259}{243 (3 x+2)^2}-\frac {49}{729 (3 x+2)^3}-\frac {740}{243} \log (3 x+2) \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 88
Rubi steps
\begin {align*} \int \frac {(1-2 x)^2 (3+5 x)^2}{(2+3 x)^4} \, dx &=\int \left (\frac {100}{81}+\frac {49}{81 (2+3 x)^4}-\frac {518}{81 (2+3 x)^3}+\frac {503}{27 (2+3 x)^2}-\frac {740}{81 (2+3 x)}\right ) \, dx\\ &=\frac {100 x}{81}-\frac {49}{729 (2+3 x)^3}+\frac {259}{243 (2+3 x)^2}-\frac {503}{81 (2+3 x)}-\frac {740}{243} \log (2+3 x)\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.02, size = 46, normalized size = 0.94 \[ \frac {24300 x^4+64800 x^3+24057 x^2-23193 x-2220 (3 x+2)^3 \log (3 x+2)-11803}{729 (3 x+2)^3} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.85, size = 62, normalized size = 1.27 \[ \frac {24300 \, x^{4} + 48600 \, x^{3} - 8343 \, x^{2} - 2220 \, {\left (27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right )} \log \left (3 \, x + 2\right ) - 44793 \, x - 16603}{729 \, {\left (27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.92, size = 32, normalized size = 0.65 \[ \frac {100}{81} \, x - \frac {40743 \, x^{2} + 51993 \, x + 16603}{729 \, {\left (3 \, x + 2\right )}^{3}} - \frac {740}{243} \, \log \left ({\left | 3 \, x + 2 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.01, size = 40, normalized size = 0.82 \[ \frac {100 x}{81}-\frac {740 \ln \left (3 x +2\right )}{243}-\frac {49}{729 \left (3 x +2\right )^{3}}+\frac {259}{243 \left (3 x +2\right )^{2}}-\frac {503}{81 \left (3 x +2\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.56, size = 41, normalized size = 0.84 \[ \frac {100}{81} \, x - \frac {40743 \, x^{2} + 51993 \, x + 16603}{729 \, {\left (27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right )}} - \frac {740}{243} \, \log \left (3 \, x + 2\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 1.12, size = 37, normalized size = 0.76 \[ \frac {100\,x}{81}-\frac {740\,\ln \left (x+\frac {2}{3}\right )}{243}-\frac {\frac {503\,x^2}{243}+\frac {5777\,x}{2187}+\frac {16603}{19683}}{x^3+2\,x^2+\frac {4\,x}{3}+\frac {8}{27}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.15, size = 41, normalized size = 0.84 \[ \frac {100 x}{81} + \frac {- 40743 x^{2} - 51993 x - 16603}{19683 x^{3} + 39366 x^{2} + 26244 x + 5832} - \frac {740 \log {\left (3 x + 2 \right )}}{243} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________