Optimal. Leaf size=14 \[ \frac {(a+b x)^{10}}{10 b} \]
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Rubi [A] time = 0.01, antiderivative size = 14, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 29, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.069, Rules used = {2059, 32} \[ \frac {(a+b x)^{10}}{10 b} \]
Antiderivative was successfully verified.
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Rule 32
Rule 2059
Rubi steps
\begin {align*} \int \left (a^3+3 a^2 b x+3 a b^2 x^2+b^3 x^3\right )^3 \, dx &=\int (a+b x)^9 \, dx\\ &=\frac {(a+b x)^{10}}{10 b}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 14, normalized size = 1.00 \[ \frac {(a+b x)^{10}}{10 b} \]
Antiderivative was successfully verified.
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fricas [B] time = 0.46, size = 97, normalized size = 6.93 \[ \frac {1}{10} x^{10} b^{9} + x^{9} b^{8} a + \frac {9}{2} x^{8} b^{7} a^{2} + 12 x^{7} b^{6} a^{3} + 21 x^{6} b^{5} a^{4} + \frac {126}{5} x^{5} b^{4} a^{5} + 21 x^{4} b^{3} a^{6} + 12 x^{3} b^{2} a^{7} + \frac {9}{2} x^{2} b a^{8} + x a^{9} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.25, size = 97, normalized size = 6.93 \[ \frac {1}{10} \, b^{9} x^{10} + a b^{8} x^{9} + \frac {9}{2} \, a^{2} b^{7} x^{8} + 12 \, a^{3} b^{6} x^{7} + 21 \, a^{4} b^{5} x^{6} + \frac {126}{5} \, a^{5} b^{4} x^{5} + 21 \, a^{6} b^{3} x^{4} + 12 \, a^{7} b^{2} x^{3} + \frac {9}{2} \, a^{8} b x^{2} + a^{9} x \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.00, size = 98, normalized size = 7.00 \[ \frac {1}{10} b^{9} x^{10}+a \,b^{8} x^{9}+\frac {9}{2} a^{2} b^{7} x^{8}+12 a^{3} b^{6} x^{7}+21 a^{4} b^{5} x^{6}+\frac {126}{5} a^{5} b^{4} x^{5}+21 a^{6} b^{3} x^{4}+12 a^{7} b^{2} x^{3}+\frac {9}{2} a^{8} b \,x^{2}+a^{9} x \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.69, size = 216, normalized size = 15.43 \[ \frac {1}{10} \, b^{9} x^{10} + a b^{8} x^{9} + \frac {27}{8} \, a^{2} b^{7} x^{8} + \frac {27}{7} \, a^{3} b^{6} x^{7} + \frac {27}{4} \, a^{6} b^{3} x^{4} + a^{9} x + \frac {3}{4} \, {\left (b^{3} x^{4} + 4 \, a b^{2} x^{3} + 6 \, a^{2} b x^{2}\right )} a^{6} + \frac {9}{10} \, {\left (5 \, b^{3} x^{6} + 18 \, a b^{2} x^{5}\right )} a^{4} b^{2} + \frac {3}{70} \, {\left (10 \, b^{6} x^{7} + 70 \, a b^{5} x^{6} + 126 \, a^{2} b^{4} x^{5} + 210 \, a^{4} b^{2} x^{3} + 21 \, {\left (4 \, b^{3} x^{5} + 15 \, a b^{2} x^{4}\right )} a^{2} b\right )} a^{3} + \frac {9}{56} \, {\left (7 \, b^{6} x^{8} + 48 \, a b^{5} x^{7} + 84 \, a^{2} b^{4} x^{6}\right )} a^{2} b \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 2.07, size = 97, normalized size = 6.93 \[ a^9\,x+\frac {9\,a^8\,b\,x^2}{2}+12\,a^7\,b^2\,x^3+21\,a^6\,b^3\,x^4+\frac {126\,a^5\,b^4\,x^5}{5}+21\,a^4\,b^5\,x^6+12\,a^3\,b^6\,x^7+\frac {9\,a^2\,b^7\,x^8}{2}+a\,b^8\,x^9+\frac {b^9\,x^{10}}{10} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.09, size = 107, normalized size = 7.64 \[ a^{9} x + \frac {9 a^{8} b x^{2}}{2} + 12 a^{7} b^{2} x^{3} + 21 a^{6} b^{3} x^{4} + \frac {126 a^{5} b^{4} x^{5}}{5} + 21 a^{4} b^{5} x^{6} + 12 a^{3} b^{6} x^{7} + \frac {9 a^{2} b^{7} x^{8}}{2} + a b^{8} x^{9} + \frac {b^{9} x^{10}}{10} \]
Verification of antiderivative is not currently implemented for this CAS.
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