Optimal. Leaf size=42 \[ \frac{1500 x^7}{7}+\frac{1100 x^6}{3}+19 x^5-\frac{1091 x^4}{4}-111 x^3+\frac{135 x^2}{2}+54 x \]
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Rubi [A] time = 0.0167219, antiderivative size = 42, 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} \[ \frac{1500 x^7}{7}+\frac{1100 x^6}{3}+19 x^5-\frac{1091 x^4}{4}-111 x^3+\frac{135 x^2}{2}+54 x \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin{align*} \int (1-2 x)^2 (2+3 x) (3+5 x)^3 \, dx &=\int \left (54+135 x-333 x^2-1091 x^3+95 x^4+2200 x^5+1500 x^6\right ) \, dx\\ &=54 x+\frac{135 x^2}{2}-111 x^3-\frac{1091 x^4}{4}+19 x^5+\frac{1100 x^6}{3}+\frac{1500 x^7}{7}\\ \end{align*}
Mathematica [A] time = 0.0008545, size = 42, normalized size = 1. \[ \frac{1500 x^7}{7}+\frac{1100 x^6}{3}+19 x^5-\frac{1091 x^4}{4}-111 x^3+\frac{135 x^2}{2}+54 x \]
Antiderivative was successfully verified.
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Maple [A] time = 0.001, size = 35, normalized size = 0.8 \begin{align*} 54\,x+{\frac{135\,{x}^{2}}{2}}-111\,{x}^{3}-{\frac{1091\,{x}^{4}}{4}}+19\,{x}^{5}+{\frac{1100\,{x}^{6}}{3}}+{\frac{1500\,{x}^{7}}{7}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.11102, size = 46, normalized size = 1.1 \begin{align*} \frac{1500}{7} \, x^{7} + \frac{1100}{3} \, x^{6} + 19 \, x^{5} - \frac{1091}{4} \, x^{4} - 111 \, x^{3} + \frac{135}{2} \, x^{2} + 54 \, x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.46575, size = 103, normalized size = 2.45 \begin{align*} \frac{1500}{7} x^{7} + \frac{1100}{3} x^{6} + 19 x^{5} - \frac{1091}{4} x^{4} - 111 x^{3} + \frac{135}{2} x^{2} + 54 x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.060016, size = 39, normalized size = 0.93 \begin{align*} \frac{1500 x^{7}}{7} + \frac{1100 x^{6}}{3} + 19 x^{5} - \frac{1091 x^{4}}{4} - 111 x^{3} + \frac{135 x^{2}}{2} + 54 x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 2.59593, size = 46, normalized size = 1.1 \begin{align*} \frac{1500}{7} \, x^{7} + \frac{1100}{3} \, x^{6} + 19 \, x^{5} - \frac{1091}{4} \, x^{4} - 111 \, x^{3} + \frac{135}{2} \, x^{2} + 54 \, x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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