Optimal. Leaf size=43 \[ \frac {b^3 x^3}{3}+\frac {3}{5} b^2 c x^5+\frac {3}{7} b c^2 x^7+\frac {c^3 x^9}{9} \]
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Rubi [A] time = 0.02, antiderivative size = 43, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 2, integrand size = 17, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.118, Rules used = {1584, 270} \[ \frac {3}{5} b^2 c x^5+\frac {b^3 x^3}{3}+\frac {3}{7} b c^2 x^7+\frac {c^3 x^9}{9} \]
Antiderivative was successfully verified.
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Rule 270
Rule 1584
Rubi steps
\begin {align*} \int \frac {\left (b x^2+c x^4\right )^3}{x^4} \, dx &=\int x^2 \left (b+c x^2\right )^3 \, dx\\ &=\int \left (b^3 x^2+3 b^2 c x^4+3 b c^2 x^6+c^3 x^8\right ) \, dx\\ &=\frac {b^3 x^3}{3}+\frac {3}{5} b^2 c x^5+\frac {3}{7} b c^2 x^7+\frac {c^3 x^9}{9}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 43, normalized size = 1.00 \[ \frac {b^3 x^3}{3}+\frac {3}{5} b^2 c x^5+\frac {3}{7} b c^2 x^7+\frac {c^3 x^9}{9} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.84, size = 35, normalized size = 0.81 \[ \frac {1}{9} \, c^{3} x^{9} + \frac {3}{7} \, b c^{2} x^{7} + \frac {3}{5} \, b^{2} c x^{5} + \frac {1}{3} \, b^{3} x^{3} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.17, size = 35, normalized size = 0.81 \[ \frac {1}{9} \, c^{3} x^{9} + \frac {3}{7} \, b c^{2} x^{7} + \frac {3}{5} \, b^{2} c x^{5} + \frac {1}{3} \, b^{3} x^{3} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 36, normalized size = 0.84 \[ \frac {1}{9} c^{3} x^{9}+\frac {3}{7} b \,c^{2} x^{7}+\frac {3}{5} b^{2} c \,x^{5}+\frac {1}{3} b^{3} x^{3} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.34, size = 35, normalized size = 0.81 \[ \frac {1}{9} \, c^{3} x^{9} + \frac {3}{7} \, b c^{2} x^{7} + \frac {3}{5} \, b^{2} c x^{5} + \frac {1}{3} \, b^{3} x^{3} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 35, normalized size = 0.81 \[ \frac {b^3\,x^3}{3}+\frac {3\,b^2\,c\,x^5}{5}+\frac {3\,b\,c^2\,x^7}{7}+\frac {c^3\,x^9}{9} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.09, size = 39, normalized size = 0.91 \[ \frac {b^{3} x^{3}}{3} + \frac {3 b^{2} c x^{5}}{5} + \frac {3 b c^{2} x^{7}}{7} + \frac {c^{3} x^{9}}{9} \]
Verification of antiderivative is not currently implemented for this CAS.
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