Optimal. Leaf size=16 \[ \frac {x^5}{3 \sqrt {c x^4}} \]
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Rubi [A] time = 0.00, antiderivative size = 16, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 3, integrand size = 23, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.130, Rules used = {1, 15, 30} \[ \frac {x^5}{3 \sqrt {c x^4}} \]
Antiderivative was successfully verified.
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Rule 1
Rule 15
Rule 30
Rubi steps
\begin {align*} \int \frac {x^4}{\sqrt {2+2 a-2 (1+a)+c x^4}} \, dx &=\int \frac {x^4}{\sqrt {c x^4}} \, dx\\ &=\frac {x^2 \int x^2 \, dx}{\sqrt {c x^4}}\\ &=\frac {x^5}{3 \sqrt {c x^4}}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 16, normalized size = 1.00 \[ \frac {x^5}{3 \sqrt {c x^4}} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.83, size = 13, normalized size = 0.81 \[ \frac {\sqrt {c x^{4}} x}{3 \, c} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 8, normalized size = 0.50 \[ \frac {x^{3}}{3 \, \sqrt {c}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 13, normalized size = 0.81 \[ \frac {x^{5}}{3 \sqrt {c \,x^{4}}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.96, size = 12, normalized size = 0.75 \[ \frac {x^{5}}{3 \, \sqrt {c x^{4}}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [F] time = 0.00, size = -1, normalized size = -0.06 \[ \int \frac {x^4}{\sqrt {c\,x^4}} \,d x \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.63, size = 15, normalized size = 0.94 \[ \frac {x^{5}}{3 \sqrt {c} \sqrt {x^{4}}} \]
Verification of antiderivative is not currently implemented for this CAS.
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