Optimal. Leaf size=23 \[ -\frac {\sqrt [3]{a x^3+b x^6}}{a x^2} \]
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Rubi [A] time = 0.00, antiderivative size = 23, normalized size of antiderivative = 1.00, 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 = {2000} \begin {gather*} -\frac {\sqrt [3]{a x^3+b x^6}}{a x^2} \end {gather*}
Antiderivative was successfully verified.
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Rule 2000
Rubi steps
\begin {align*} \int \frac {1}{\left (a x^3+b x^6\right )^{2/3}} \, dx &=-\frac {\sqrt [3]{a x^3+b x^6}}{a x^2}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 23, normalized size = 1.00 \begin {gather*} -\frac {\sqrt [3]{x^3 \left (a+b x^3\right )}}{a x^2} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [A] time = 0.41, size = 23, normalized size = 1.00 \begin {gather*} -\frac {\sqrt [3]{a x^3+b x^6}}{a x^2} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 1.17, size = 21, normalized size = 0.91 \begin {gather*} -\frac {{\left (b x^{6} + a x^{3}\right )}^{\frac {1}{3}}}{a x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 25.00, size = 14, normalized size = 0.61 \begin {gather*} -\frac {{\left (b + \frac {a}{x^{3}}\right )}^{\frac {1}{3}}}{a} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 27, normalized size = 1.17 \begin {gather*} -\frac {\left (b \,x^{3}+a \right ) x}{\left (b \,x^{6}+a \,x^{3}\right )^{\frac {2}{3}} a} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.45, size = 17, normalized size = 0.74 \begin {gather*} -\frac {{\left (b x^{3} + a\right )}^{\frac {1}{3}}}{a x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.15, size = 21, normalized size = 0.91 \begin {gather*} -\frac {{\left (b\,x^6+a\,x^3\right )}^{1/3}}{a\,x^2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {1}{\left (a x^{3} + b x^{6}\right )^{\frac {2}{3}}}\, dx \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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