Optimal. Leaf size=107 \[ 64 a^2 e^4 x-\frac {16}{5} e^2 x^5 \left (d^4-8 a e^3\right )-8 a d^3 e^2 x^2+32 a d e^4 x^4+\frac {d^6 x^3}{3}-\frac {8}{3} d^3 e^3 x^6+\frac {64}{7} d^2 e^4 x^7+16 d e^5 x^8+\frac {64 e^6 x^9}{9} \]
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Rubi [A] time = 0.05, antiderivative size = 107, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 32, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.031, Rules used = {2061} \[ 64 a^2 e^4 x-\frac {16}{5} e^2 x^5 \left (d^4-8 a e^3\right )-8 a d^3 e^2 x^2+32 a d e^4 x^4+\frac {64}{7} d^2 e^4 x^7-\frac {8}{3} d^3 e^3 x^6+\frac {d^6 x^3}{3}+16 d e^5 x^8+\frac {64 e^6 x^9}{9} \]
Antiderivative was successfully verified.
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Rule 2061
Rubi steps
\begin {align*} \int \left (8 a e^2-d^3 x+8 d e^2 x^3+8 e^3 x^4\right )^2 \, dx &=\int \left (64 a^2 e^4-16 a d^3 e^2 x+d^6 x^2+128 a d e^4 x^3-16 e^2 \left (d^4-8 a e^3\right ) x^4-16 d^3 e^3 x^5+64 d^2 e^4 x^6+128 d e^5 x^7+64 e^6 x^8\right ) \, dx\\ &=64 a^2 e^4 x-8 a d^3 e^2 x^2+\frac {d^6 x^3}{3}+32 a d e^4 x^4-\frac {16}{5} e^2 \left (d^4-8 a e^3\right ) x^5-\frac {8}{3} d^3 e^3 x^6+\frac {64}{7} d^2 e^4 x^7+16 d e^5 x^8+\frac {64 e^6 x^9}{9}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 109, normalized size = 1.02 \[ 64 a^2 e^4 x+\frac {16}{5} e^2 x^5 \left (8 a e^3-d^4\right )-8 a d^3 e^2 x^2+32 a d e^4 x^4+\frac {d^6 x^3}{3}-\frac {8}{3} d^3 e^3 x^6+\frac {64}{7} d^2 e^4 x^7+16 d e^5 x^8+\frac {64 e^6 x^9}{9} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.39, size = 99, normalized size = 0.93 \[ \frac {64}{9} x^{9} e^{6} + 16 x^{8} e^{5} d + \frac {64}{7} x^{7} e^{4} d^{2} - \frac {8}{3} x^{6} e^{3} d^{3} - \frac {16}{5} x^{5} e^{2} d^{4} + \frac {128}{5} x^{5} e^{5} a + 32 x^{4} e^{4} d a + \frac {1}{3} x^{3} d^{6} - 8 x^{2} e^{2} d^{3} a + 64 x e^{4} a^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.29, size = 90, normalized size = 0.84 \[ \frac {64}{9} \, x^{9} e^{6} + 16 \, d x^{8} e^{5} + \frac {64}{7} \, d^{2} x^{7} e^{4} - \frac {8}{3} \, d^{3} x^{6} e^{3} - \frac {16}{5} \, d^{4} x^{5} e^{2} + \frac {1}{3} \, d^{6} x^{3} + \frac {128}{5} \, a x^{5} e^{5} + 32 \, a d x^{4} e^{4} - 8 \, a d^{3} x^{2} e^{2} + 64 \, a^{2} x e^{4} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 100, normalized size = 0.93 \[ \frac {64 e^{6} x^{9}}{9}+16 d \,e^{5} x^{8}+\frac {64 d^{2} e^{4} x^{7}}{7}-\frac {8 d^{3} e^{3} x^{6}}{3}+32 a d \,e^{4} x^{4}+\frac {d^{6} x^{3}}{3}-8 a \,d^{3} e^{2} x^{2}+64 a^{2} e^{4} x +\frac {\left (128 a \,e^{5}-16 d^{4} e^{2}\right ) x^{5}}{5} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.61, size = 101, normalized size = 0.94 \[ \frac {64}{9} \, e^{6} x^{9} + 16 \, d e^{5} x^{8} + \frac {64}{7} \, d^{2} e^{4} x^{7} + \frac {1}{3} \, d^{6} x^{3} + 64 \, a^{2} e^{4} x - \frac {8}{15} \, {\left (5 \, e^{3} x^{6} + 6 \, d e^{2} x^{5}\right )} d^{3} + \frac {8}{5} \, {\left (16 \, e^{3} x^{5} + 20 \, d e^{2} x^{4} - 5 \, d^{3} x^{2}\right )} a e^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 98, normalized size = 0.92 \[ x^5\,\left (\frac {128\,a\,e^5}{5}-\frac {16\,d^4\,e^2}{5}\right )+\frac {d^6\,x^3}{3}+\frac {64\,e^6\,x^9}{9}+64\,a^2\,e^4\,x+16\,d\,e^5\,x^8-\frac {8\,d^3\,e^3\,x^6}{3}+\frac {64\,d^2\,e^4\,x^7}{7}-8\,a\,d^3\,e^2\,x^2+32\,a\,d\,e^4\,x^4 \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.09, size = 112, normalized size = 1.05 \[ 64 a^{2} e^{4} x - 8 a d^{3} e^{2} x^{2} + 32 a d e^{4} x^{4} + \frac {d^{6} x^{3}}{3} - \frac {8 d^{3} e^{3} x^{6}}{3} + \frac {64 d^{2} e^{4} x^{7}}{7} + 16 d e^{5} x^{8} + \frac {64 e^{6} x^{9}}{9} + x^{5} \left (\frac {128 a e^{5}}{5} - \frac {16 d^{4} e^{2}}{5}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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