Optimal. Leaf size=34 \[ -\frac{5}{108} (3 x+2)^8+\frac{37}{189} (3 x+2)^7-\frac{7}{162} (3 x+2)^6 \]
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Rubi [A] time = 0.0176127, antiderivative size = 34, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 18, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.056, Rules used = {77} \[ -\frac{5}{108} (3 x+2)^8+\frac{37}{189} (3 x+2)^7-\frac{7}{162} (3 x+2)^6 \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin{align*} \int (1-2 x) (2+3 x)^5 (3+5 x) \, dx &=\int \left (-\frac{7}{9} (2+3 x)^5+\frac{37}{9} (2+3 x)^6-\frac{10}{9} (2+3 x)^7\right ) \, dx\\ &=-\frac{7}{162} (2+3 x)^6+\frac{37}{189} (2+3 x)^7-\frac{5}{108} (2+3 x)^8\\ \end{align*}
Mathematica [A] time = 0.0020148, size = 47, normalized size = 1.38 \[ -\frac{1215 x^8}{4}-\frac{8343 x^7}{7}-\frac{3627 x^6}{2}-1170 x^5+30 x^4+\frac{1600 x^3}{3}+344 x^2+96 x \]
Antiderivative was successfully verified.
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Maple [A] time = 0.001, size = 40, normalized size = 1.2 \begin{align*} -{\frac{1215\,{x}^{8}}{4}}-{\frac{8343\,{x}^{7}}{7}}-{\frac{3627\,{x}^{6}}{2}}-1170\,{x}^{5}+30\,{x}^{4}+{\frac{1600\,{x}^{3}}{3}}+344\,{x}^{2}+96\,x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.21518, size = 53, normalized size = 1.56 \begin{align*} -\frac{1215}{4} \, x^{8} - \frac{8343}{7} \, x^{7} - \frac{3627}{2} \, x^{6} - 1170 \, x^{5} + 30 \, x^{4} + \frac{1600}{3} \, x^{3} + 344 \, x^{2} + 96 \, x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.36712, size = 120, normalized size = 3.53 \begin{align*} -\frac{1215}{4} x^{8} - \frac{8343}{7} x^{7} - \frac{3627}{2} x^{6} - 1170 x^{5} + 30 x^{4} + \frac{1600}{3} x^{3} + 344 x^{2} + 96 x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.062024, size = 44, normalized size = 1.29 \begin{align*} - \frac{1215 x^{8}}{4} - \frac{8343 x^{7}}{7} - \frac{3627 x^{6}}{2} - 1170 x^{5} + 30 x^{4} + \frac{1600 x^{3}}{3} + 344 x^{2} + 96 x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 3.75204, size = 53, normalized size = 1.56 \begin{align*} -\frac{1215}{4} \, x^{8} - \frac{8343}{7} \, x^{7} - \frac{3627}{2} \, x^{6} - 1170 \, x^{5} + 30 \, x^{4} + \frac{1600}{3} \, x^{3} + 344 \, x^{2} + 96 \, x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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