Optimal. Leaf size=43 \[ \frac{3}{5} b^2 c x^5+\frac{b^3 x^4}{4}+\frac{1}{2} b c^2 x^6+\frac{c^3 x^7}{7} \]
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Rubi [A] time = 0.0146033, antiderivative size = 43, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.091, Rules used = {611} \[ \frac{3}{5} b^2 c x^5+\frac{b^3 x^4}{4}+\frac{1}{2} b c^2 x^6+\frac{c^3 x^7}{7} \]
Antiderivative was successfully verified.
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Rule 611
Rubi steps
\begin{align*} \int \left (b x+c x^2\right )^3 \, dx &=\int \left (b^3 x^3+3 b^2 c x^4+3 b c^2 x^5+c^3 x^6\right ) \, dx\\ &=\frac{b^3 x^4}{4}+\frac{3}{5} b^2 c x^5+\frac{1}{2} b c^2 x^6+\frac{c^3 x^7}{7}\\ \end{align*}
Mathematica [A] time = 0.0020258, size = 43, normalized size = 1. \[ \frac{3}{5} b^2 c x^5+\frac{b^3 x^4}{4}+\frac{1}{2} b c^2 x^6+\frac{c^3 x^7}{7} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.041, size = 36, normalized size = 0.8 \begin{align*}{\frac{{b}^{3}{x}^{4}}{4}}+{\frac{3\,{b}^{2}c{x}^{5}}{5}}+{\frac{b{c}^{2}{x}^{6}}{2}}+{\frac{{c}^{3}{x}^{7}}{7}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.12471, size = 47, normalized size = 1.09 \begin{align*} \frac{1}{7} \, c^{3} x^{7} + \frac{1}{2} \, b c^{2} x^{6} + \frac{3}{5} \, b^{2} c x^{5} + \frac{1}{4} \, b^{3} x^{4} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.33609, size = 80, normalized size = 1.86 \begin{align*} \frac{1}{7} x^{7} c^{3} + \frac{1}{2} x^{6} c^{2} b + \frac{3}{5} x^{5} c b^{2} + \frac{1}{4} x^{4} b^{3} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.153519, size = 37, normalized size = 0.86 \begin{align*} \frac{b^{3} x^{4}}{4} + \frac{3 b^{2} c x^{5}}{5} + \frac{b c^{2} x^{6}}{2} + \frac{c^{3} x^{7}}{7} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.28007, size = 47, normalized size = 1.09 \begin{align*} \frac{1}{7} \, c^{3} x^{7} + \frac{1}{2} \, b c^{2} x^{6} + \frac{3}{5} \, b^{2} c x^{5} + \frac{1}{4} \, b^{3} x^{4} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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