Optimal. Leaf size=16 \[ \frac {x \left (a+\frac {b}{\sqrt [3]{x}}\right )^3}{a} \]
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Rubi [A] time = 0.01, antiderivative size = 16, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.182, Rules used = {190, 37} \[ \frac {x \left (a+\frac {b}{\sqrt [3]{x}}\right )^3}{a} \]
Antiderivative was successfully verified.
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Rule 37
Rule 190
Rubi steps
\begin {align*} \int \left (a+\frac {b}{\sqrt [3]{x}}\right )^2 \, dx &=-\left (3 \operatorname {Subst}\left (\int \frac {(a+b x)^2}{x^4} \, dx,x,\frac {1}{\sqrt [3]{x}}\right )\right )\\ &=\frac {\left (a+\frac {b}{\sqrt [3]{x}}\right )^3 x}{a}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 25, normalized size = 1.56 \[ a^2 x+3 a b x^{2/3}+3 b^2 \sqrt [3]{x} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.91, size = 21, normalized size = 1.31 \[ a^{2} x + 3 \, a b x^{\frac {2}{3}} + 3 \, b^{2} x^{\frac {1}{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.16, size = 21, normalized size = 1.31 \[ a^{2} x + 3 \, a b x^{\frac {2}{3}} + 3 \, b^{2} x^{\frac {1}{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 14, normalized size = 0.88 \[ \frac {\left (a \,x^{\frac {1}{3}}+b \right )^{3}}{a} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.61, size = 21, normalized size = 1.31 \[ a^{2} x + 3 \, a b x^{\frac {2}{3}} + 3 \, b^{2} x^{\frac {1}{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 21, normalized size = 1.31 \[ a^2\,x+3\,b^2\,x^{1/3}+3\,a\,b\,x^{2/3} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.19, size = 24, normalized size = 1.50 \[ a^{2} x + 3 a b x^{\frac {2}{3}} + 3 b^{2} \sqrt [3]{x} \]
Verification of antiderivative is not currently implemented for this CAS.
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