Optimal. Leaf size=20 \[ \frac {2 \sqrt {a x^3-b}}{3 a} \]
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Rubi [A] time = 0.01, antiderivative size = 20, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 17, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.059, Rules used = {261} \begin {gather*} \frac {2 \sqrt {a x^3-b}}{3 a} \end {gather*}
Antiderivative was successfully verified.
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Rule 261
Rubi steps
\begin {align*} \int \frac {x^2}{\sqrt {-b+a x^3}} \, dx &=\frac {2 \sqrt {-b+a x^3}}{3 a}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 20, normalized size = 1.00 \begin {gather*} \frac {2 \sqrt {a x^3-b}}{3 a} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [A] time = 0.02, size = 20, normalized size = 1.00 \begin {gather*} \frac {2 \sqrt {-b+a x^3}}{3 a} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.46, size = 16, normalized size = 0.80 \begin {gather*} \frac {2 \, \sqrt {a x^{3} - b}}{3 \, a} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.28, size = 16, normalized size = 0.80 \begin {gather*} \frac {2 \, \sqrt {a x^{3} - b}}{3 \, a} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.30, size = 17, normalized size = 0.85
method | result | size |
gosper | \(\frac {2 \sqrt {a \,x^{3}-b}}{3 a}\) | \(17\) |
derivativedivides | \(\frac {2 \sqrt {a \,x^{3}-b}}{3 a}\) | \(17\) |
default | \(\frac {2 \sqrt {a \,x^{3}-b}}{3 a}\) | \(17\) |
trager | \(\frac {2 \sqrt {a \,x^{3}-b}}{3 a}\) | \(17\) |
risch | \(\frac {2 \sqrt {a \,x^{3}-b}}{3 a}\) | \(17\) |
elliptic | \(\frac {2 \sqrt {a \,x^{3}-b}}{3 a}\) | \(17\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.42, size = 16, normalized size = 0.80 \begin {gather*} \frac {2 \, \sqrt {a x^{3} - b}}{3 \, a} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.30, size = 16, normalized size = 0.80 \begin {gather*} \frac {2\,\sqrt {a\,x^3-b}}{3\,a} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.36, size = 26, normalized size = 1.30 \begin {gather*} \begin {cases} \frac {2 \sqrt {a x^{3} - b}}{3 a} & \text {for}\: a \neq 0 \\\frac {x^{3}}{3 \sqrt {- b}} & \text {otherwise} \end {cases} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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