Optimal. Leaf size=45 \[ -\frac{9 a^2 b}{5 x^{5/3}}-\frac{a^3}{2 x^2}-\frac{9 a b^2}{4 x^{4/3}}-\frac{b^3}{x} \]
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Rubi [A] time = 0.0191243, antiderivative size = 45, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.133, Rules used = {266, 43} \[ -\frac{9 a^2 b}{5 x^{5/3}}-\frac{a^3}{2 x^2}-\frac{9 a b^2}{4 x^{4/3}}-\frac{b^3}{x} \]
Antiderivative was successfully verified.
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Rule 266
Rule 43
Rubi steps
\begin{align*} \int \frac{\left (a+b \sqrt [3]{x}\right )^3}{x^3} \, dx &=3 \operatorname{Subst}\left (\int \frac{(a+b x)^3}{x^7} \, dx,x,\sqrt [3]{x}\right )\\ &=3 \operatorname{Subst}\left (\int \left (\frac{a^3}{x^7}+\frac{3 a^2 b}{x^6}+\frac{3 a b^2}{x^5}+\frac{b^3}{x^4}\right ) \, dx,x,\sqrt [3]{x}\right )\\ &=-\frac{a^3}{2 x^2}-\frac{9 a^2 b}{5 x^{5/3}}-\frac{9 a b^2}{4 x^{4/3}}-\frac{b^3}{x}\\ \end{align*}
Mathematica [A] time = 0.0157946, size = 41, normalized size = 0.91 \[ -\frac{36 a^2 b \sqrt [3]{x}+10 a^3+45 a b^2 x^{2/3}+20 b^3 x}{20 x^2} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.005, size = 36, normalized size = 0.8 \begin{align*} -{\frac{{a}^{3}}{2\,{x}^{2}}}-{\frac{9\,b{a}^{2}}{5}{x}^{-{\frac{5}{3}}}}-{\frac{9\,{b}^{2}a}{4}{x}^{-{\frac{4}{3}}}}-{\frac{{b}^{3}}{x}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.963843, size = 47, normalized size = 1.04 \begin{align*} -\frac{20 \, b^{3} x + 45 \, a b^{2} x^{\frac{2}{3}} + 36 \, a^{2} b x^{\frac{1}{3}} + 10 \, a^{3}}{20 \, x^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.42144, size = 93, normalized size = 2.07 \begin{align*} -\frac{20 \, b^{3} x + 45 \, a b^{2} x^{\frac{2}{3}} + 36 \, a^{2} b x^{\frac{1}{3}} + 10 \, a^{3}}{20 \, x^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 1.40515, size = 41, normalized size = 0.91 \begin{align*} - \frac{a^{3}}{2 x^{2}} - \frac{9 a^{2} b}{5 x^{\frac{5}{3}}} - \frac{9 a b^{2}}{4 x^{\frac{4}{3}}} - \frac{b^{3}}{x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.10696, size = 47, normalized size = 1.04 \begin{align*} -\frac{20 \, b^{3} x + 45 \, a b^{2} x^{\frac{2}{3}} + 36 \, a^{2} b x^{\frac{1}{3}} + 10 \, a^{3}}{20 \, x^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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