Optimal. Leaf size=56 \[ -\frac{250 (3 x+2)^9}{2187}+\frac{1025 (3 x+2)^8}{1944}-\frac{185}{567} (3 x+2)^7+\frac{107 (3 x+2)^6}{1458}-\frac{7 (3 x+2)^5}{1215} \]
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Rubi [A] time = 0.0234432, antiderivative size = 56, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.05, Rules used = {77} \[ -\frac{250 (3 x+2)^9}{2187}+\frac{1025 (3 x+2)^8}{1944}-\frac{185}{567} (3 x+2)^7+\frac{107 (3 x+2)^6}{1458}-\frac{7 (3 x+2)^5}{1215} \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin{align*} \int (1-2 x) (2+3 x)^4 (3+5 x)^3 \, dx &=\int \left (-\frac{7}{81} (2+3 x)^4+\frac{107}{81} (2+3 x)^5-\frac{185}{27} (2+3 x)^6+\frac{1025}{81} (2+3 x)^7-\frac{250}{81} (2+3 x)^8\right ) \, dx\\ &=-\frac{7 (2+3 x)^5}{1215}+\frac{107 (2+3 x)^6}{1458}-\frac{185}{567} (2+3 x)^7+\frac{1025 (2+3 x)^8}{1944}-\frac{250 (2+3 x)^9}{2187}\\ \end{align*}
Mathematica [A] time = 0.0019635, size = 52, normalized size = 0.93 \[ -2250 x^9-\frac{80325 x^8}{8}-\frac{127845 x^7}{7}-\frac{32453 x^6}{2}-\frac{25237 x^5}{5}+3452 x^4+4296 x^3+1944 x^2+432 x \]
Antiderivative was successfully verified.
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Maple [A] time = 0.001, size = 45, normalized size = 0.8 \begin{align*} -2250\,{x}^{9}-{\frac{80325\,{x}^{8}}{8}}-{\frac{127845\,{x}^{7}}{7}}-{\frac{32453\,{x}^{6}}{2}}-{\frac{25237\,{x}^{5}}{5}}+3452\,{x}^{4}+4296\,{x}^{3}+1944\,{x}^{2}+432\,x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.06779, size = 59, normalized size = 1.05 \begin{align*} -2250 \, x^{9} - \frac{80325}{8} \, x^{8} - \frac{127845}{7} \, x^{7} - \frac{32453}{2} \, x^{6} - \frac{25237}{5} \, x^{5} + 3452 \, x^{4} + 4296 \, x^{3} + 1944 \, x^{2} + 432 \, x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.56031, size = 147, normalized size = 2.62 \begin{align*} -2250 x^{9} - \frac{80325}{8} x^{8} - \frac{127845}{7} x^{7} - \frac{32453}{2} x^{6} - \frac{25237}{5} x^{5} + 3452 x^{4} + 4296 x^{3} + 1944 x^{2} + 432 x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.065698, size = 49, normalized size = 0.88 \begin{align*} - 2250 x^{9} - \frac{80325 x^{8}}{8} - \frac{127845 x^{7}}{7} - \frac{32453 x^{6}}{2} - \frac{25237 x^{5}}{5} + 3452 x^{4} + 4296 x^{3} + 1944 x^{2} + 432 x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 2.05281, size = 59, normalized size = 1.05 \begin{align*} -2250 \, x^{9} - \frac{80325}{8} \, x^{8} - \frac{127845}{7} \, x^{7} - \frac{32453}{2} \, x^{6} - \frac{25237}{5} \, x^{5} + 3452 \, x^{4} + 4296 \, x^{3} + 1944 \, x^{2} + 432 \, x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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