Optimal. Leaf size=30 \[ \frac {a^2 x^3}{3}+\frac {2}{5} a b x^5+\frac {b^2 x^7}{7} \]
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Rubi [A] time = 0.01, antiderivative size = 30, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.077, Rules used = {270} \begin {gather*} \frac {a^2 x^3}{3}+\frac {2}{5} a b x^5+\frac {b^2 x^7}{7} \end {gather*}
Antiderivative was successfully verified.
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Rule 270
Rubi steps
\begin {align*} \int x^2 \left (a+b x^2\right )^2 \, dx &=\int \left (a^2 x^2+2 a b x^4+b^2 x^6\right ) \, dx\\ &=\frac {a^2 x^3}{3}+\frac {2}{5} a b x^5+\frac {b^2 x^7}{7}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 30, normalized size = 1.00 \begin {gather*} \frac {a^2 x^3}{3}+\frac {2}{5} a b x^5+\frac {b^2 x^7}{7} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int x^2 \left (a+b x^2\right )^2 \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 0.92, size = 24, normalized size = 0.80 \begin {gather*} \frac {1}{7} x^{7} b^{2} + \frac {2}{5} x^{5} b a + \frac {1}{3} x^{3} a^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.13, size = 24, normalized size = 0.80 \begin {gather*} \frac {1}{7} \, b^{2} x^{7} + \frac {2}{5} \, a b x^{5} + \frac {1}{3} \, a^{2} x^{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 25, normalized size = 0.83 \begin {gather*} \frac {1}{7} b^{2} x^{7}+\frac {2}{5} a b \,x^{5}+\frac {1}{3} a^{2} x^{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.35, size = 24, normalized size = 0.80 \begin {gather*} \frac {1}{7} \, b^{2} x^{7} + \frac {2}{5} \, a b x^{5} + \frac {1}{3} \, a^{2} x^{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 24, normalized size = 0.80 \begin {gather*} \frac {a^2\,x^3}{3}+\frac {2\,a\,b\,x^5}{5}+\frac {b^2\,x^7}{7} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.07, size = 26, normalized size = 0.87 \begin {gather*} \frac {a^{2} x^{3}}{3} + \frac {2 a b x^{5}}{5} + \frac {b^{2} x^{7}}{7} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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