Optimal. Leaf size=35 \[ b^3 x+b^2 c x^3+\frac {3}{5} b c^2 x^5+\frac {c^3 x^7}{7} \]
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Rubi [A] time = 0.02, antiderivative size = 35, 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, 194} \[ b^2 c x^3+b^3 x+\frac {3}{5} b c^2 x^5+\frac {c^3 x^7}{7} \]
Antiderivative was successfully verified.
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Rule 194
Rule 1584
Rubi steps
\begin {align*} \int \frac {\left (b x^2+c x^4\right )^3}{x^6} \, dx &=\int \left (b+c x^2\right )^3 \, dx\\ &=\int \left (b^3+3 b^2 c x^2+3 b c^2 x^4+c^3 x^6\right ) \, dx\\ &=b^3 x+b^2 c x^3+\frac {3}{5} b c^2 x^5+\frac {c^3 x^7}{7}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 35, normalized size = 1.00 \[ b^3 x+b^2 c x^3+\frac {3}{5} b c^2 x^5+\frac {c^3 x^7}{7} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.80, size = 31, normalized size = 0.89 \[ \frac {1}{7} \, c^{3} x^{7} + \frac {3}{5} \, b c^{2} x^{5} + b^{2} c x^{3} + b^{3} x \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.16, size = 31, normalized size = 0.89 \[ \frac {1}{7} \, c^{3} x^{7} + \frac {3}{5} \, b c^{2} x^{5} + b^{2} c x^{3} + b^{3} x \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 32, normalized size = 0.91 \[ \frac {1}{7} c^{3} x^{7}+\frac {3}{5} b \,c^{2} x^{5}+b^{2} c \,x^{3}+b^{3} x \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.32, size = 31, normalized size = 0.89 \[ \frac {1}{7} \, c^{3} x^{7} + \frac {3}{5} \, b c^{2} x^{5} + b^{2} c x^{3} + b^{3} x \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 31, normalized size = 0.89 \[ b^3\,x+b^2\,c\,x^3+\frac {3\,b\,c^2\,x^5}{5}+\frac {c^3\,x^7}{7} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.08, size = 32, normalized size = 0.91 \[ b^{3} x + b^{2} c x^{3} + \frac {3 b c^{2} x^{5}}{5} + \frac {c^{3} x^{7}}{7} \]
Verification of antiderivative is not currently implemented for this CAS.
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