Optimal. Leaf size=56 \[ -\frac{100}{243 (3 x+2)}+\frac{370}{243 (3 x+2)^2}-\frac{503}{243 (3 x+2)^3}+\frac{259}{486 (3 x+2)^4}-\frac{49}{1215 (3 x+2)^5} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0200987, antiderivative size = 56, normalized size of antiderivative = 1., 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} \[ -\frac{100}{243 (3 x+2)}+\frac{370}{243 (3 x+2)^2}-\frac{503}{243 (3 x+2)^3}+\frac{259}{486 (3 x+2)^4}-\frac{49}{1215 (3 x+2)^5} \]
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)^6} \, dx &=\int \left (\frac{49}{81 (2+3 x)^6}-\frac{518}{81 (2+3 x)^5}+\frac{503}{27 (2+3 x)^4}-\frac{740}{81 (2+3 x)^3}+\frac{100}{81 (2+3 x)^2}\right ) \, dx\\ &=-\frac{49}{1215 (2+3 x)^5}+\frac{259}{486 (2+3 x)^4}-\frac{503}{243 (2+3 x)^3}+\frac{370}{243 (2+3 x)^2}-\frac{100}{243 (2+3 x)}\\ \end{align*}
Mathematica [A] time = 0.0126215, size = 31, normalized size = 0.55 \[ -\frac{81000 x^4+116100 x^3+61470 x^2+19275 x+4028}{2430 (3 x+2)^5} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.005, size = 47, normalized size = 0.8 \begin{align*} -{\frac{49}{1215\, \left ( 2+3\,x \right ) ^{5}}}+{\frac{259}{486\, \left ( 2+3\,x \right ) ^{4}}}-{\frac{503}{243\, \left ( 2+3\,x \right ) ^{3}}}+{\frac{370}{243\, \left ( 2+3\,x \right ) ^{2}}}-{\frac{100}{486+729\,x}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 1.04817, size = 66, normalized size = 1.18 \begin{align*} -\frac{81000 \, x^{4} + 116100 \, x^{3} + 61470 \, x^{2} + 19275 \, x + 4028}{2430 \,{\left (243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.44801, size = 158, normalized size = 2.82 \begin{align*} -\frac{81000 \, x^{4} + 116100 \, x^{3} + 61470 \, x^{2} + 19275 \, x + 4028}{2430 \,{\left (243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 0.148324, size = 46, normalized size = 0.82 \begin{align*} - \frac{81000 x^{4} + 116100 x^{3} + 61470 x^{2} + 19275 x + 4028}{590490 x^{5} + 1968300 x^{4} + 2624400 x^{3} + 1749600 x^{2} + 583200 x + 77760} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 4.69699, size = 39, normalized size = 0.7 \begin{align*} -\frac{81000 \, x^{4} + 116100 \, x^{3} + 61470 \, x^{2} + 19275 \, x + 4028}{2430 \,{\left (3 \, x + 2\right )}^{5}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]