Optimal. Leaf size=40 \[ -\frac{2250 x^7}{7}-\frac{1975 x^6}{2}-1061 x^5-\frac{1111 x^4}{4}+345 x^3+324 x^2+108 x \]
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Rubi [A] time = 0.0176297, antiderivative size = 40, 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} \[ -\frac{2250 x^7}{7}-\frac{1975 x^6}{2}-1061 x^5-\frac{1111 x^4}{4}+345 x^3+324 x^2+108 x \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin{align*} \int (1-2 x) (2+3 x)^2 (3+5 x)^3 \, dx &=\int \left (108+648 x+1035 x^2-1111 x^3-5305 x^4-5925 x^5-2250 x^6\right ) \, dx\\ &=108 x+324 x^2+345 x^3-\frac{1111 x^4}{4}-1061 x^5-\frac{1975 x^6}{2}-\frac{2250 x^7}{7}\\ \end{align*}
Mathematica [A] time = 0.0009116, size = 40, normalized size = 1. \[ -\frac{2250 x^7}{7}-\frac{1975 x^6}{2}-1061 x^5-\frac{1111 x^4}{4}+345 x^3+324 x^2+108 x \]
Antiderivative was successfully verified.
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Maple [A] time = 0.001, size = 35, normalized size = 0.9 \begin{align*} 108\,x+324\,{x}^{2}+345\,{x}^{3}-{\frac{1111\,{x}^{4}}{4}}-1061\,{x}^{5}-{\frac{1975\,{x}^{6}}{2}}-{\frac{2250\,{x}^{7}}{7}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.01578, size = 46, normalized size = 1.15 \begin{align*} -\frac{2250}{7} \, x^{7} - \frac{1975}{2} \, x^{6} - 1061 \, x^{5} - \frac{1111}{4} \, x^{4} + 345 \, x^{3} + 324 \, x^{2} + 108 \, x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.58774, size = 105, normalized size = 2.62 \begin{align*} -\frac{2250}{7} x^{7} - \frac{1975}{2} x^{6} - 1061 x^{5} - \frac{1111}{4} x^{4} + 345 x^{3} + 324 x^{2} + 108 x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.062326, size = 37, normalized size = 0.92 \begin{align*} - \frac{2250 x^{7}}{7} - \frac{1975 x^{6}}{2} - 1061 x^{5} - \frac{1111 x^{4}}{4} + 345 x^{3} + 324 x^{2} + 108 x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.47852, size = 46, normalized size = 1.15 \begin{align*} -\frac{2250}{7} \, x^{7} - \frac{1975}{2} \, x^{6} - 1061 \, x^{5} - \frac{1111}{4} \, x^{4} + 345 \, x^{3} + 324 \, x^{2} + 108 \, x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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