Optimal. Leaf size=35 \[ a^3 x+a^2 c x^3+\frac {3}{5} a c^2 x^5+\frac {c^3 x^7}{7} \]
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Rubi [A] time = 0.01, antiderivative size = 35, 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} \[ a^2 c x^3+a^3 x+\frac {3}{5} a c^2 x^5+\frac {c^3 x^7}{7} \]
Antiderivative was successfully verified.
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Rule 194
Rubi steps
\begin {align*} \int \left (a+c x^2\right )^3 \, dx &=\int \left (a^3+3 a^2 c x^2+3 a c^2 x^4+c^3 x^6\right ) \, dx\\ &=a^3 x+a^2 c x^3+\frac {3}{5} a c^2 x^5+\frac {c^3 x^7}{7}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 35, normalized size = 1.00 \[ a^3 x+a^2 c x^3+\frac {3}{5} a c^2 x^5+\frac {c^3 x^7}{7} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.75, size = 31, normalized size = 0.89 \[ \frac {1}{7} x^{7} c^{3} + \frac {3}{5} x^{5} c^{2} a + x^{3} c a^{2} + x a^{3} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.53, size = 31, normalized size = 0.89 \[ \frac {1}{7} \, c^{3} x^{7} + \frac {3}{5} \, a c^{2} x^{5} + a^{2} c x^{3} + a^{3} x \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 32, normalized size = 0.91 \[ \frac {1}{7} c^{3} x^{7}+\frac {3}{5} a \,c^{2} x^{5}+a^{2} c \,x^{3}+a^{3} x \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.35, size = 31, normalized size = 0.89 \[ \frac {1}{7} \, c^{3} x^{7} + \frac {3}{5} \, a c^{2} x^{5} + a^{2} c x^{3} + a^{3} x \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 31, normalized size = 0.89 \[ a^3\,x+a^2\,c\,x^3+\frac {3\,a\,c^2\,x^5}{5}+\frac {c^3\,x^7}{7} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.07, size = 32, normalized size = 0.91 \[ a^{3} x + a^{2} c x^{3} + \frac {3 a c^{2} x^{5}}{5} + \frac {c^{3} x^{7}}{7} \]
Verification of antiderivative is not currently implemented for this CAS.
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