Optimal. Leaf size=21 \[ -\frac{\left (a+b \sqrt [3]{x}\right )^6}{2 a x^2} \]
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Rubi [A] time = 0.0033234, antiderivative size = 21, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.067, Rules used = {264} \[ -\frac{\left (a+b \sqrt [3]{x}\right )^6}{2 a x^2} \]
Antiderivative was successfully verified.
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Rule 264
Rubi steps
\begin{align*} \int \frac{\left (a+b \sqrt [3]{x}\right )^5}{x^3} \, dx &=-\frac{\left (a+b \sqrt [3]{x}\right )^6}{2 a x^2}\\ \end{align*}
Mathematica [A] time = 0.00401, size = 21, normalized size = 1. \[ -\frac{\left (a+b \sqrt [3]{x}\right )^6}{2 a x^2} \]
Antiderivative was successfully verified.
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Maple [B] time = 0.007, size = 58, normalized size = 2.8 \begin{align*} -10\,{\frac{{a}^{2}{b}^{3}}{x}}-3\,{\frac{{a}^{4}b}{{x}^{5/3}}}-{\frac{15\,{a}^{3}{b}^{2}}{2}{x}^{-{\frac{4}{3}}}}-{\frac{15\,a{b}^{4}}{2}{x}^{-{\frac{2}{3}}}}-{\frac{{a}^{5}}{2\,{x}^{2}}}-3\,{\frac{{b}^{5}}{\sqrt [3]{x}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] time = 1.03246, size = 74, normalized size = 3.52 \begin{align*} -\frac{6 \, b^{5} x^{\frac{5}{3}} + 15 \, a b^{4} x^{\frac{4}{3}} + 20 \, a^{2} b^{3} x + 15 \, a^{3} b^{2} x^{\frac{2}{3}} + 6 \, a^{4} b x^{\frac{1}{3}} + a^{5}}{2 \, x^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] time = 1.49597, size = 134, normalized size = 6.38 \begin{align*} -\frac{20 \, a^{2} b^{3} x + a^{5} + 3 \,{\left (2 \, b^{5} x + 5 \, a^{3} b^{2}\right )} x^{\frac{2}{3}} + 3 \,{\left (5 \, a b^{4} x + 2 \, a^{4} b\right )} x^{\frac{1}{3}}}{2 \, x^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] time = 1.31962, size = 70, normalized size = 3.33 \begin{align*} - \frac{a^{5}}{2 x^{2}} - \frac{3 a^{4} b}{x^{\frac{5}{3}}} - \frac{15 a^{3} b^{2}}{2 x^{\frac{4}{3}}} - \frac{10 a^{2} b^{3}}{x} - \frac{15 a b^{4}}{2 x^{\frac{2}{3}}} - \frac{3 b^{5}}{\sqrt [3]{x}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [B] time = 1.23521, size = 74, normalized size = 3.52 \begin{align*} -\frac{6 \, b^{5} x^{\frac{5}{3}} + 15 \, a b^{4} x^{\frac{4}{3}} + 20 \, a^{2} b^{3} x + 15 \, a^{3} b^{2} x^{\frac{2}{3}} + 6 \, a^{4} b x^{\frac{1}{3}} + a^{5}}{2 \, x^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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