Optimal. Leaf size=16 \[ \frac {\left (a+b x^2\right )^4}{8 b} \]
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Rubi [A] time = 0.00, antiderivative size = 16, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.091, Rules used = {261} \begin {gather*} \frac {\left (a+b x^2\right )^4}{8 b} \end {gather*}
Antiderivative was successfully verified.
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Rule 261
Rubi steps
\begin {align*} \int x \left (a+b x^2\right )^3 \, dx &=\frac {\left (a+b x^2\right )^4}{8 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 )^4}{8 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+b x^2\right )^3 \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [B] time = 0.89, size = 35, normalized size = 2.19 \begin {gather*} \frac {1}{8} x^{8} b^{3} + \frac {1}{2} x^{6} b^{2} a + \frac {3}{4} x^{4} b a^{2} + \frac {1}{2} x^{2} a^{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.00, size = 14, normalized size = 0.88 \begin {gather*} \frac {{\left (b x^{2} + a\right )}^{4}}{8 \, b} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.00, size = 36, normalized size = 2.25 \begin {gather*} \frac {1}{8} b^{3} x^{8}+\frac {1}{2} a \,b^{2} x^{6}+\frac {3}{4} a^{2} b \,x^{4}+\frac {1}{2} a^{3} x^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.34, size = 14, normalized size = 0.88 \begin {gather*} \frac {{\left (b x^{2} + a\right )}^{4}}{8 \, b} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.06, size = 35, normalized size = 2.19 \begin {gather*} \frac {a^3\,x^2}{2}+\frac {3\,a^2\,b\,x^4}{4}+\frac {a\,b^2\,x^6}{2}+\frac {b^3\,x^8}{8} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.07, size = 37, normalized size = 2.31 \begin {gather*} \frac {a^{3} x^{2}}{2} + \frac {3 a^{2} b x^{4}}{4} + \frac {a b^{2} x^{6}}{2} + \frac {b^{3} x^{8}}{8} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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