Optimal. Leaf size=34 \[ \frac {2}{375} (5 x+3)^6-\frac {44}{625} (5 x+3)^5+\frac {121}{500} (5 x+3)^4 \]
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Rubi [A] time = 0.01, antiderivative size = 34, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 15, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.067, Rules used = {43} \begin {gather*} \frac {2}{375} (5 x+3)^6-\frac {44}{625} (5 x+3)^5+\frac {121}{500} (5 x+3)^4 \end {gather*}
Antiderivative was successfully verified.
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Rule 43
Rubi steps
\begin {align*} \int (1-2 x)^2 (3+5 x)^3 \, dx &=\int \left (\frac {121}{25} (3+5 x)^3-\frac {44}{25} (3+5 x)^4+\frac {4}{25} (3+5 x)^5\right ) \, dx\\ &=\frac {121}{500} (3+5 x)^4-\frac {44}{625} (3+5 x)^5+\frac {2}{375} (3+5 x)^6\\ \end {align*}
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Mathematica [A] time = 0.00, size = 35, normalized size = 1.03 \begin {gather*} \frac {250 x^6}{3}+80 x^5-\frac {235 x^4}{4}-69 x^3+\frac {27 x^2}{2}+27 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 (3+5 x)^3 \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 1.17, size = 29, normalized size = 0.85 \begin {gather*} \frac {250}{3} x^{6} + 80 x^{5} - \frac {235}{4} x^{4} - 69 x^{3} + \frac {27}{2} x^{2} + 27 x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.96, size = 29, normalized size = 0.85 \begin {gather*} \frac {250}{3} \, x^{6} + 80 \, x^{5} - \frac {235}{4} \, x^{4} - 69 \, x^{3} + \frac {27}{2} \, x^{2} + 27 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 30, normalized size = 0.88 \begin {gather*} \frac {250}{3} x^{6}+80 x^{5}-\frac {235}{4} x^{4}-69 x^{3}+\frac {27}{2} x^{2}+27 x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.52, size = 29, normalized size = 0.85 \begin {gather*} \frac {250}{3} \, x^{6} + 80 \, x^{5} - \frac {235}{4} \, x^{4} - 69 \, x^{3} + \frac {27}{2} \, x^{2} + 27 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.02, size = 29, normalized size = 0.85 \begin {gather*} \frac {250\,x^6}{3}+80\,x^5-\frac {235\,x^4}{4}-69\,x^3+\frac {27\,x^2}{2}+27\,x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.07, size = 32, normalized size = 0.94 \begin {gather*} \frac {250 x^{6}}{3} + 80 x^{5} - \frac {235 x^{4}}{4} - 69 x^{3} + \frac {27 x^{2}}{2} + 27 x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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