Optimal. Leaf size=5 \[ \frac {x}{c^2} \]
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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}
\begin {gather*} \frac {x}{c^2} \end {gather*}
Antiderivative was successfully verified.
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Rule 8
Rule 27
Rubi steps
\begin {align*} \int \frac {(d+e x)^4}{\left (c d^2+2 c d e x+c e^2 x^2\right )^2} \, dx &=\int \frac {1}{c^2} \, dx\\ &=\frac {x}{c^2}\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 5, normalized size = 1.00 \begin {gather*} \frac {x}{c^2} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.59, size = 6, normalized size = 1.20
method | result | size |
default | \(\frac {x}{c^{2}}\) | \(6\) |
risch | \(\frac {x}{c^{2}}\) | \(6\) |
norman | \(\frac {\frac {e^{3} x^{4}}{c}+\frac {d^{3} x}{c}+\frac {3 e^{2} d \,x^{3}}{c}+\frac {3 e \,d^{2} x^{2}}{c}}{c \left (e x +d \right )^{3}}\) | \(55\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.29, size = 5, normalized size = 1.00 \begin {gather*} \frac {x}{c^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 2.87, size = 5, normalized size = 1.00 \begin {gather*} \frac {x}{c^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.02, size = 3, normalized size = 0.60 \begin {gather*} \frac {x}{c^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.73, size = 5, normalized size = 1.00 \begin {gather*} \frac {x}{c^{2}} \end {gather*}
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 \begin {gather*} \frac {x}{c^2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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