Optimal. Leaf size=14 \[ \frac{(a+b x)^{10}}{10 b} \]
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Rubi [A] time = 0.0074009, antiderivative size = 14, normalized size of antiderivative = 1., 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 2059
Rule 32
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*}
Mathematica [A] time = 0.0009253, size = 14, normalized size = 1. \[ \frac{(a+b x)^{10}}{10 b} \]
Antiderivative was successfully verified.
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Maple [B] time = 0.002, size = 98, normalized size = 7. \begin{align*}{\frac{{b}^{9}{x}^{10}}{10}}+a{b}^{8}{x}^{9}+{\frac{9\,{a}^{2}{b}^{7}{x}^{8}}{2}}+12\,{a}^{3}{b}^{6}{x}^{7}+21\,{a}^{4}{b}^{5}{x}^{6}+{\frac{126\,{a}^{5}{b}^{4}{x}^{5}}{5}}+21\,{a}^{6}{b}^{3}{x}^{4}+12\,{a}^{7}{b}^{2}{x}^{3}+{\frac{9\,{a}^{8}b{x}^{2}}{2}}+{a}^{9}x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] time = 1.16856, size = 292, normalized size = 20.86 \begin{align*} \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 \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] time = 1.11428, size = 212, normalized size = 15.14 \begin{align*} \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} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] time = 0.083674, size = 107, normalized size = 7.64 \begin{align*} 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} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [B] time = 1.06108, size = 131, normalized size = 9.36 \begin{align*} \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 \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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