Optimal. Leaf size=34 \[ -\frac{1}{125} (5 x+3)^6+\frac{31}{625} (5 x+3)^5+\frac{11}{500} (5 x+3)^4 \]
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Rubi [A] time = 0.0154868, 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} \[ -\frac{1}{125} (5 x+3)^6+\frac{31}{625} (5 x+3)^5+\frac{11}{500} (5 x+3)^4 \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin{align*} \int (1-2 x) (2+3 x) (3+5 x)^3 \, dx &=\int \left (\frac{11}{25} (3+5 x)^3+\frac{31}{25} (3+5 x)^4-\frac{6}{25} (3+5 x)^5\right ) \, dx\\ &=\frac{11}{500} (3+5 x)^4+\frac{31}{625} (3+5 x)^5-\frac{1}{125} (3+5 x)^6\\ \end{align*}
Mathematica [A] time = 0.0008309, size = 33, normalized size = 0.97 \[ -125 x^6-295 x^5-\frac{785 x^4}{4}+51 x^3+\frac{243 x^2}{2}+54 x \]
Antiderivative was successfully verified.
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Maple [A] time = 0.001, size = 30, normalized size = 0.9 \begin{align*} -125\,{x}^{6}-295\,{x}^{5}-{\frac{785\,{x}^{4}}{4}}+51\,{x}^{3}+{\frac{243\,{x}^{2}}{2}}+54\,x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 2.07235, size = 39, normalized size = 1.15 \begin{align*} -125 \, x^{6} - 295 \, x^{5} - \frac{785}{4} \, x^{4} + 51 \, x^{3} + \frac{243}{2} \, x^{2} + 54 \, x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.48861, size = 81, normalized size = 2.38 \begin{align*} -125 x^{6} - 295 x^{5} - \frac{785}{4} x^{4} + 51 x^{3} + \frac{243}{2} x^{2} + 54 x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.058122, size = 31, normalized size = 0.91 \begin{align*} - 125 x^{6} - 295 x^{5} - \frac{785 x^{4}}{4} + 51 x^{3} + \frac{243 x^{2}}{2} + 54 x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.99047, size = 39, normalized size = 1.15 \begin{align*} -125 \, x^{6} - 295 \, x^{5} - \frac{785}{4} \, x^{4} + 51 \, x^{3} + \frac{243}{2} \, x^{2} + 54 \, x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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