Optimal. Leaf size=72 \[ a^2 x+\frac {2}{5} (64-a) x^5-2 (16-a) x^4+\frac {16}{3} (4-a) x^3+8 a x^2+\frac {x^9}{9}-x^8+\frac {32 x^7}{7}-\frac {40 x^6}{3} \]
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Rubi [A] time = 0.03, antiderivative size = 72, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 22, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.045, Rules used = {2061} \[ a^2 x+\frac {2}{5} (64-a) x^5-2 (16-a) x^4+\frac {16}{3} (4-a) x^3+8 a x^2+\frac {x^9}{9}-x^8+\frac {32 x^7}{7}-\frac {40 x^6}{3} \]
Antiderivative was successfully verified.
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Rule 2061
Rubi steps
\begin {align*} \int \left (a+8 x-8 x^2+4 x^3-x^4\right )^2 \, dx &=\int \left (a^2+16 a x+16 (4-a) x^2-8 (16-a) x^3+2 (64-a) x^4-80 x^5+32 x^6-8 x^7+x^8\right ) \, dx\\ &=a^2 x+8 a x^2+\frac {16}{3} (4-a) x^3-2 (16-a) x^4+\frac {2}{5} (64-a) x^5-\frac {40 x^6}{3}+\frac {32 x^7}{7}-x^8+\frac {x^9}{9}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 66, normalized size = 0.92 \[ a^2 x-\frac {2}{5} (a-64) x^5+2 (a-16) x^4-\frac {16}{3} (a-4) x^3+8 a x^2+\frac {x^9}{9}-x^8+\frac {32 x^7}{7}-\frac {40 x^6}{3} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.37, size = 65, normalized size = 0.90 \[ \frac {1}{9} x^{9} - x^{8} + \frac {32}{7} x^{7} - \frac {40}{3} x^{6} - \frac {2}{5} x^{5} a + \frac {128}{5} x^{5} + 2 x^{4} a - 32 x^{4} - \frac {16}{3} x^{3} a + \frac {64}{3} x^{3} + 8 x^{2} a + x a^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.31, size = 65, normalized size = 0.90 \[ \frac {1}{9} \, x^{9} - x^{8} + \frac {32}{7} \, x^{7} - \frac {2}{5} \, a x^{5} - \frac {40}{3} \, x^{6} + 2 \, a x^{4} + \frac {128}{5} \, x^{5} - \frac {16}{3} \, a x^{3} - 32 \, x^{4} + a^{2} x + 8 \, a x^{2} + \frac {64}{3} \, x^{3} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 63, normalized size = 0.88 \[ \frac {x^{9}}{9}-x^{8}+\frac {32 x^{7}}{7}-\frac {40 x^{6}}{3}+\frac {\left (-2 a +128\right ) x^{5}}{5}+\frac {\left (8 a -128\right ) x^{4}}{4}+a^{2} x +8 a \,x^{2}+\frac {\left (-16 a +64\right ) x^{3}}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.71, size = 65, normalized size = 0.90 \[ \frac {1}{9} \, x^{9} - x^{8} + \frac {32}{7} \, x^{7} - \frac {40}{3} \, x^{6} + \frac {128}{5} \, x^{5} - 32 \, x^{4} + a^{2} x + \frac {64}{3} \, x^{3} - \frac {2}{15} \, {\left (3 \, x^{5} - 15 \, x^{4} + 40 \, x^{3} - 60 \, x^{2}\right )} a \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 61, normalized size = 0.85 \[ x^4\,\left (2\,a-32\right )-x^3\,\left (\frac {16\,a}{3}-\frac {64}{3}\right )-x^5\,\left (\frac {2\,a}{5}-\frac {128}{5}\right )+8\,a\,x^2+a^2\,x-\frac {40\,x^6}{3}+\frac {32\,x^7}{7}-x^8+\frac {x^9}{9} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.08, size = 65, normalized size = 0.90 \[ a^{2} x + 8 a x^{2} + \frac {x^{9}}{9} - x^{8} + \frac {32 x^{7}}{7} - \frac {40 x^{6}}{3} + x^{5} \left (\frac {128}{5} - \frac {2 a}{5}\right ) + x^{4} \left (2 a - 32\right ) + x^{3} \left (\frac {64}{3} - \frac {16 a}{3}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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