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 = 0.02, antiderivative size = 42, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.050, Rules used = {77} \begin {gather*} \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 {gather*}
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*}
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Mathematica [A] time = 0.00, size = 42, normalized size = 1.00 \begin {gather*} \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 {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int (1-2 x)^2 (2+3 x) (3+5 x)^3 \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 1.58, size = 34, normalized size = 0.81 \begin {gather*} \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 {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.94, size = 34, normalized size = 0.81 \begin {gather*} \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 {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 35, normalized size = 0.83 \begin {gather*} \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 {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.64, size = 34, normalized size = 0.81 \begin {gather*} \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 {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 34, normalized size = 0.81 \begin {gather*} \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 {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.07, size = 39, normalized size = 0.93 \begin {gather*} \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 {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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