Optimal. Leaf size=14 \[ \frac{(a+b x)^7}{7 b} \]
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Rubi [A] time = 0.007188, 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} \[ \frac{(a+b x)^7}{7 b} \]
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 )^2 \, dx &=\int (a+b x)^6 \, dx\\ &=\frac{(a+b x)^7}{7 b}\\ \end{align*}
Mathematica [A] time = 0.0010834, size = 14, normalized size = 1. \[ \frac{(a+b x)^7}{7 b} \]
Antiderivative was successfully verified.
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Maple [B] time = 0., size = 65, normalized size = 4.6 \begin{align*}{\frac{{b}^{6}{x}^{7}}{7}}+a{b}^{5}{x}^{6}+3\,{a}^{2}{b}^{4}{x}^{5}+5\,{a}^{3}{b}^{3}{x}^{4}+5\,{a}^{4}{b}^{2}{x}^{3}+3\,{a}^{5}b{x}^{2}+{a}^{6}x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] time = 1.16221, size = 134, normalized size = 9.57 \begin{align*} \frac{1}{7} \, b^{6} x^{7} + a b^{5} x^{6} + \frac{9}{5} \, a^{2} b^{4} x^{5} + 3 \, a^{4} b^{2} x^{3} + a^{6} x + \frac{1}{2} \,{\left (b^{3} x^{4} + 4 \, a b^{2} x^{3} + 6 \, a^{2} b x^{2}\right )} a^{3} + \frac{3}{10} \,{\left (4 \, b^{3} x^{5} + 15 \, a b^{2} x^{4}\right )} a^{2} b \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] time = 1.08018, size = 128, normalized size = 9.14 \begin{align*} \frac{1}{7} x^{7} b^{6} + x^{6} b^{5} a + 3 x^{5} b^{4} a^{2} + 5 x^{4} b^{3} a^{3} + 5 x^{3} b^{2} a^{4} + 3 x^{2} b a^{5} + x a^{6} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] time = 0.073416, size = 66, normalized size = 4.71 \begin{align*} a^{6} x + 3 a^{5} b x^{2} + 5 a^{4} b^{2} x^{3} + 5 a^{3} b^{3} x^{4} + 3 a^{2} b^{4} x^{5} + a b^{5} x^{6} + \frac{b^{6} x^{7}}{7} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [B] time = 1.06185, size = 86, normalized size = 6.14 \begin{align*} \frac{1}{7} \, b^{6} x^{7} + a b^{5} x^{6} + 3 \, a^{2} b^{4} x^{5} + 5 \, a^{3} b^{3} x^{4} + 5 \, a^{4} b^{2} x^{3} + 3 \, a^{5} b x^{2} + a^{6} x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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