Optimal. Leaf size=8 \[ \frac {c x^3}{3} \]
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Rubi [A] time = 0.00, antiderivative size = 8, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 23, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.087, Rules used = {21, 30} \[ \frac {c x^3}{3} \]
Antiderivative was successfully verified.
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Rule 21
Rule 30
Rubi steps
\begin {align*} \int \frac {x^2 \left (a c+b c x^2\right )}{a+b x^2} \, dx &=c \int x^2 \, dx\\ &=\frac {c x^3}{3}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 8, normalized size = 1.00 \[ \frac {c x^3}{3} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.45, size = 6, normalized size = 0.75 \[ \frac {1}{3} \, c x^{3} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.34, size = 6, normalized size = 0.75 \[ \frac {1}{3} \, c x^{3} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 7, normalized size = 0.88 \[ \frac {c \,x^{3}}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.97, size = 6, normalized size = 0.75 \[ \frac {1}{3} \, c x^{3} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.01, size = 6, normalized size = 0.75 \[ \frac {c\,x^3}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.07, size = 5, normalized size = 0.62 \[ \frac {c x^{3}}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
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