Optimal. Leaf size=44 \[ \frac {16}{9 (3 x+2)}-\frac {91}{54 (3 x+2)^2}+\frac {49}{243 (3 x+2)^3}+\frac {20}{81} \log (3 x+2) \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.02, antiderivative size = 44, 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} \[ \frac {16}{9 (3 x+2)}-\frac {91}{54 (3 x+2)^2}+\frac {49}{243 (3 x+2)^3}+\frac {20}{81} \log (3 x+2) \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 77
Rubi steps
\begin {align*} \int \frac {(1-2 x)^2 (3+5 x)}{(2+3 x)^4} \, dx &=\int \left (-\frac {49}{27 (2+3 x)^4}+\frac {91}{9 (2+3 x)^3}-\frac {16}{3 (2+3 x)^2}+\frac {20}{27 (2+3 x)}\right ) \, dx\\ &=\frac {49}{243 (2+3 x)^3}-\frac {91}{54 (2+3 x)^2}+\frac {16}{9 (2+3 x)}+\frac {20}{81} \log (2+3 x)\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.02, size = 36, normalized size = 0.82 \[ \frac {7776 x^2+7911 x+120 (3 x+2)^3 \log (3 x+2)+1916}{486 (3 x+2)^3} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.60, size = 52, normalized size = 1.18 \[ \frac {7776 \, x^{2} + 120 \, {\left (27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right )} \log \left (3 \, x + 2\right ) + 7911 \, x + 1916}{486 \, {\left (27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 1.16, size = 29, normalized size = 0.66 \[ \frac {7776 \, x^{2} + 7911 \, x + 1916}{486 \, {\left (3 \, x + 2\right )}^{3}} + \frac {20}{81} \, \log \left ({\left | 3 \, x + 2 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.01, size = 37, normalized size = 0.84 \[ \frac {20 \ln \left (3 x +2\right )}{81}+\frac {49}{243 \left (3 x +2\right )^{3}}-\frac {91}{54 \left (3 x +2\right )^{2}}+\frac {16}{9 \left (3 x +2\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.59, size = 38, normalized size = 0.86 \[ \frac {7776 \, x^{2} + 7911 \, x + 1916}{486 \, {\left (27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right )}} + \frac {20}{81} \, \log \left (3 \, x + 2\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.03, size = 33, normalized size = 0.75 \[ \frac {20\,\ln \left (x+\frac {2}{3}\right )}{81}+\frac {\frac {16\,x^2}{27}+\frac {293\,x}{486}+\frac {958}{6561}}{x^3+2\,x^2+\frac {4\,x}{3}+\frac {8}{27}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.13, size = 34, normalized size = 0.77 \[ \frac {7776 x^{2} + 7911 x + 1916}{13122 x^{3} + 26244 x^{2} + 17496 x + 3888} + \frac {20 \log {\left (3 x + 2 \right )}}{81} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________