Optimal. Leaf size=25 \[ a^2 x+\frac {2}{3} a c x^3+\frac {c^2 x^5}{5} \]
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Rubi [A] time = 0.01, antiderivative size = 25, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 9, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.111, Rules used = {194} \[ a^2 x+\frac {2}{3} a c x^3+\frac {c^2 x^5}{5} \]
Antiderivative was successfully verified.
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Rule 194
Rubi steps
\begin {align*} \int \left (a+c x^2\right )^2 \, dx &=\int \left (a^2+2 a c x^2+c^2 x^4\right ) \, dx\\ &=a^2 x+\frac {2}{3} a c x^3+\frac {c^2 x^5}{5}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 25, normalized size = 1.00 \[ a^2 x+\frac {2}{3} a c x^3+\frac {c^2 x^5}{5} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.73, size = 21, normalized size = 0.84 \[ \frac {1}{5} x^{5} c^{2} + \frac {2}{3} x^{3} c a + x a^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.43, size = 21, normalized size = 0.84 \[ \frac {1}{5} \, c^{2} x^{5} + \frac {2}{3} \, a c x^{3} + a^{2} x \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 22, normalized size = 0.88 \[ \frac {1}{5} c^{2} x^{5}+\frac {2}{3} a c \,x^{3}+a^{2} x \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.36, size = 21, normalized size = 0.84 \[ \frac {1}{5} \, c^{2} x^{5} + \frac {2}{3} \, a c x^{3} + a^{2} x \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 21, normalized size = 0.84 \[ a^2\,x+\frac {2\,a\,c\,x^3}{3}+\frac {c^2\,x^5}{5} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.06, size = 22, normalized size = 0.88 \[ a^{2} x + \frac {2 a c x^{3}}{3} + \frac {c^{2} x^{5}}{5} \]
Verification of antiderivative is not currently implemented for this CAS.
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