Optimal. Leaf size=16 \[ \frac {\left (b+c x^2\right )^3}{6 c} \]
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Rubi [A] time = 0.01, antiderivative size = 16, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 17, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.118, Rules used = {1584, 261} \begin {gather*} \frac {\left (b+c x^2\right )^3}{6 c} \end {gather*}
Antiderivative was successfully verified.
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Rule 261
Rule 1584
Rubi steps
\begin {align*} \int \frac {\left (b x^2+c x^4\right )^2}{x^3} \, dx &=\int x \left (b+c x^2\right )^2 \, dx\\ &=\frac {\left (b+c x^2\right )^3}{6 c}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 16, normalized size = 1.00 \begin {gather*} \frac {\left (b+c x^2\right )^3}{6 c} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [A] time = 0.02, size = 27, normalized size = 1.69 \begin {gather*} \frac {1}{6} x^2 \left (3 b^2+3 b c x^2+c^2 x^4\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.44, size = 24, normalized size = 1.50 \begin {gather*} \frac {1}{6} \, c^{2} x^{6} + \frac {1}{2} \, b c x^{4} + \frac {1}{2} \, b^{2} x^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 24, normalized size = 1.50 \begin {gather*} \frac {1}{6} \, c^{2} x^{6} + \frac {1}{2} \, b c x^{4} + \frac {1}{2} \, b^{2} x^{2} \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 = 1.56 \begin {gather*} \frac {1}{6} c^{2} x^{6}+\frac {1}{2} b c \,x^{4}+\frac {1}{2} b^{2} x^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.31, size = 24, normalized size = 1.50 \begin {gather*} \frac {1}{6} \, c^{2} x^{6} + \frac {1}{2} \, b c x^{4} + \frac {1}{2} \, b^{2} x^{2} \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 = 1.50 \begin {gather*} \frac {b^2\,x^2}{2}+\frac {b\,c\,x^4}{2}+\frac {c^2\,x^6}{6} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.10, size = 24, normalized size = 1.50 \begin {gather*} \frac {b^{2} x^{2}}{2} + \frac {b c x^{4}}{2} + \frac {c^{2} x^{6}}{6} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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