Optimal. Leaf size=16 \[ \frac {\left (a+b x^2\right )^5}{10 b} \]
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Rubi [A] time = 0.00, antiderivative size = 16, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 22, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.091, Rules used = {28, 261} \begin {gather*} \frac {\left (a+b x^2\right )^5}{10 b} \end {gather*}
Antiderivative was successfully verified.
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Rule 28
Rule 261
Rubi steps
\begin {align*} \int x \left (a^2+2 a b x^2+b^2 x^4\right )^2 \, dx &=\frac {\int x \left (a b+b^2 x^2\right )^4 \, dx}{b^4}\\ &=\frac {\left (a+b x^2\right )^5}{10 b}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 16, normalized size = 1.00 \begin {gather*} \frac {\left (a+b x^2\right )^5}{10 b} \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 \left (a^2+2 a b x^2+b^2 x^4\right )^2 \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [B] time = 0.72, size = 44, normalized size = 2.75 \begin {gather*} \frac {1}{10} x^{10} b^{4} + \frac {1}{2} x^{8} b^{3} a + x^{6} b^{2} a^{2} + x^{4} b a^{3} + \frac {1}{2} x^{2} a^{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.15, size = 44, normalized size = 2.75 \begin {gather*} \frac {1}{10} \, b^{4} x^{10} + \frac {1}{2} \, a b^{3} x^{8} + a^{2} b^{2} x^{6} + a^{3} b x^{4} + \frac {1}{2} \, a^{4} x^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.00, size = 45, normalized size = 2.81 \begin {gather*} \frac {1}{10} b^{4} x^{10}+\frac {1}{2} a \,b^{3} x^{8}+a^{2} b^{2} x^{6}+a^{3} b \,x^{4}+\frac {1}{2} a^{4} x^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 1.33, size = 44, normalized size = 2.75 \begin {gather*} \frac {1}{10} \, b^{4} x^{10} + \frac {1}{2} \, a b^{3} x^{8} + a^{2} b^{2} x^{6} + a^{3} b x^{4} + \frac {1}{2} \, a^{4} x^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.02, size = 44, normalized size = 2.75 \begin {gather*} \frac {a^4\,x^2}{2}+a^3\,b\,x^4+a^2\,b^2\,x^6+\frac {a\,b^3\,x^8}{2}+\frac {b^4\,x^{10}}{10} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.08, size = 44, normalized size = 2.75 \begin {gather*} \frac {a^{4} x^{2}}{2} + a^{3} b x^{4} + a^{2} b^{2} x^{6} + \frac {a b^{3} x^{8}}{2} + \frac {b^{4} x^{10}}{10} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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