Optimal. Leaf size=34 \[ -\frac {a^2}{3 x^3}-\frac {3 a b}{4 x^{8/3}}-\frac {3 b^2}{7 x^{7/3}} \]
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Rubi [A] time = 0.01, antiderivative size = 34, normalized size of antiderivative = 1.00, 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} \[ -\frac {a^2}{3 x^3}-\frac {3 a b}{4 x^{8/3}}-\frac {3 b^2}{7 x^{7/3}} \]
Antiderivative was successfully verified.
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Rule 43
Rule 266
Rubi steps
\begin {align*} \int \frac {\left (a+b \sqrt [3]{x}\right )^2}{x^4} \, dx &=3 \operatorname {Subst}\left (\int \frac {(a+b x)^2}{x^{10}} \, dx,x,\sqrt [3]{x}\right )\\ &=3 \operatorname {Subst}\left (\int \left (\frac {a^2}{x^{10}}+\frac {2 a b}{x^9}+\frac {b^2}{x^8}\right ) \, dx,x,\sqrt [3]{x}\right )\\ &=-\frac {a^2}{3 x^3}-\frac {3 a b}{4 x^{8/3}}-\frac {3 b^2}{7 x^{7/3}}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 34, normalized size = 1.00 \[ -\frac {a^2}{3 x^3}-\frac {3 a b}{4 x^{8/3}}-\frac {3 b^2}{7 x^{7/3}} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.65, size = 26, normalized size = 0.76 \[ -\frac {36 \, b^{2} x^{\frac {2}{3}} + 63 \, a b x^{\frac {1}{3}} + 28 \, a^{2}}{84 \, x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 26, normalized size = 0.76 \[ -\frac {36 \, b^{2} x^{\frac {2}{3}} + 63 \, a b x^{\frac {1}{3}} + 28 \, a^{2}}{84 \, x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 25, normalized size = 0.74 \[ -\frac {3 b^{2}}{7 x^{\frac {7}{3}}}-\frac {3 a b}{4 x^{\frac {8}{3}}}-\frac {a^{2}}{3 x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.92, size = 26, normalized size = 0.76 \[ -\frac {36 \, b^{2} x^{\frac {2}{3}} + 63 \, a b x^{\frac {1}{3}} + 28 \, a^{2}}{84 \, x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 26, normalized size = 0.76 \[ -\frac {28\,a^2+36\,b^2\,x^{2/3}+63\,a\,b\,x^{1/3}}{84\,x^3} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 1.88, size = 32, normalized size = 0.94 \[ - \frac {a^{2}}{3 x^{3}} - \frac {3 a b}{4 x^{\frac {8}{3}}} - \frac {3 b^{2}}{7 x^{\frac {7}{3}}} \]
Verification of antiderivative is not currently implemented for this CAS.
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