Optimal. Leaf size=66 \[ \frac{972 x^5}{625}+\frac{648 x^4}{625}-\frac{5499 x^3}{3125}-\frac{5301 x^2}{6250}+\frac{17796 x}{15625}-\frac{1771}{390625 (5 x+3)}-\frac{121}{781250 (5 x+3)^2}+\frac{10234 \log (5 x+3)}{390625} \]
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Rubi [A] time = 0.0330502, antiderivative size = 66, 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} \[ \frac{972 x^5}{625}+\frac{648 x^4}{625}-\frac{5499 x^3}{3125}-\frac{5301 x^2}{6250}+\frac{17796 x}{15625}-\frac{1771}{390625 (5 x+3)}-\frac{121}{781250 (5 x+3)^2}+\frac{10234 \log (5 x+3)}{390625} \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin{align*} \int \frac{(1-2 x)^2 (2+3 x)^5}{(3+5 x)^3} \, dx &=\int \left (\frac{17796}{15625}-\frac{5301 x}{3125}-\frac{16497 x^2}{3125}+\frac{2592 x^3}{625}+\frac{972 x^4}{125}+\frac{121}{78125 (3+5 x)^3}+\frac{1771}{78125 (3+5 x)^2}+\frac{10234}{78125 (3+5 x)}\right ) \, dx\\ &=\frac{17796 x}{15625}-\frac{5301 x^2}{6250}-\frac{5499 x^3}{3125}+\frac{648 x^4}{625}+\frac{972 x^5}{625}-\frac{121}{781250 (3+5 x)^2}-\frac{1771}{390625 (3+5 x)}+\frac{10234 \log (3+5 x)}{390625}\\ \end{align*}
Mathematica [A] time = 0.0326632, size = 63, normalized size = 0.95 \[ \frac{151875000 x^7+283500000 x^6+4331250 x^5-252590625 x^4-50032500 x^3+161774550 x^2+109699660 x+102340 (5 x+3)^2 \log (6 (5 x+3))+20870428}{3906250 (5 x+3)^2} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.004, size = 51, normalized size = 0.8 \begin{align*}{\frac{17796\,x}{15625}}-{\frac{5301\,{x}^{2}}{6250}}-{\frac{5499\,{x}^{3}}{3125}}+{\frac{648\,{x}^{4}}{625}}+{\frac{972\,{x}^{5}}{625}}-{\frac{121}{781250\, \left ( 3+5\,x \right ) ^{2}}}-{\frac{1771}{1171875+1953125\,x}}+{\frac{10234\,\ln \left ( 3+5\,x \right ) }{390625}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.16148, size = 69, normalized size = 1.05 \begin{align*} \frac{972}{625} \, x^{5} + \frac{648}{625} \, x^{4} - \frac{5499}{3125} \, x^{3} - \frac{5301}{6250} \, x^{2} + \frac{17796}{15625} \, x - \frac{11 \,{\left (1610 \, x + 977\right )}}{781250 \,{\left (25 \, x^{2} + 30 \, x + 9\right )}} + \frac{10234}{390625} \, \log \left (5 \, x + 3\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.29611, size = 242, normalized size = 3.67 \begin{align*} \frac{30375000 \, x^{7} + 56700000 \, x^{6} + 866250 \, x^{5} - 50518125 \, x^{4} - 10006500 \, x^{3} + 20730375 \, x^{2} + 20468 \,{\left (25 \, x^{2} + 30 \, x + 9\right )} \log \left (5 \, x + 3\right ) + 7990490 \, x - 10747}{781250 \,{\left (25 \, x^{2} + 30 \, x + 9\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.125858, size = 56, normalized size = 0.85 \begin{align*} \frac{972 x^{5}}{625} + \frac{648 x^{4}}{625} - \frac{5499 x^{3}}{3125} - \frac{5301 x^{2}}{6250} + \frac{17796 x}{15625} - \frac{17710 x + 10747}{19531250 x^{2} + 23437500 x + 7031250} + \frac{10234 \log{\left (5 x + 3 \right )}}{390625} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.66543, size = 63, normalized size = 0.95 \begin{align*} \frac{972}{625} \, x^{5} + \frac{648}{625} \, x^{4} - \frac{5499}{3125} \, x^{3} - \frac{5301}{6250} \, x^{2} + \frac{17796}{15625} \, x - \frac{11 \,{\left (1610 \, x + 977\right )}}{781250 \,{\left (5 \, x + 3\right )}^{2}} + \frac{10234}{390625} \, \log \left ({\left | 5 \, x + 3 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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