Optimal. Leaf size=5 \[ \frac {x}{c^3} \]
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Rubi [A] time = 0.00, antiderivative size = 5, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 30, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.067, Rules used = {27, 8} \[ \frac {x}{c^3} \]
Antiderivative was successfully verified.
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Rule 8
Rule 27
Rubi steps
\begin {align*} \int \frac {(d+e x)^6}{\left (c d^2+2 c d e x+c e^2 x^2\right )^3} \, dx &=\int \frac {1}{c^3} \, dx\\ &=\frac {x}{c^3}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 5, normalized size = 1.00 \[ \frac {x}{c^3} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.99, size = 5, normalized size = 1.00 \[ \frac {x}{c^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [F(-2)] time = 0.00, size = 0, normalized size = 0.00 \[ \text {Exception raised: NotImplementedError} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 6, normalized size = 1.20 \[ \frac {x}{c^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.31, size = 5, normalized size = 1.00 \[ \frac {x}{c^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.01, size = 5, normalized size = 1.00 \[ \frac {x}{c^3} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.15, size = 3, normalized size = 0.60 \[ \frac {x}{c^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
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