Optimal. Leaf size=13 \[ \frac{\log (d+e x)}{c e} \]
[Out]
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Rubi [A] time = 0.0158584, antiderivative size = 13, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 3, integrand size = 28, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.107 \[ \frac{\log (d+e x)}{c e} \]
Antiderivative was successfully verified.
[In] Int[(d + e*x)/(c*d^2 + 2*c*d*e*x + c*e^2*x^2),x]
[Out]
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Rubi in Sympy [A] time = 16.7933, size = 8, normalized size = 0.62 \[ \frac{\log{\left (d + e x \right )}}{c e} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((e*x+d)/(c*e**2*x**2+2*c*d*e*x+c*d**2),x)
[Out]
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Mathematica [A] time = 0.00305904, size = 16, normalized size = 1.23 \[ \frac{\log (c d+c e x)}{c e} \]
Antiderivative was successfully verified.
[In] Integrate[(d + e*x)/(c*d^2 + 2*c*d*e*x + c*e^2*x^2),x]
[Out]
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Maple [A] time = 0.002, size = 14, normalized size = 1.1 \[{\frac{\ln \left ( ex+d \right ) }{ce}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((e*x+d)/(c*e^2*x^2+2*c*d*e*x+c*d^2),x)
[Out]
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Maxima [A] time = 0.697949, size = 39, normalized size = 3. \[ \frac{\log \left (c e^{2} x^{2} + 2 \, c d e x + c d^{2}\right )}{2 \, c e} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((e*x + d)/(c*e^2*x^2 + 2*c*d*e*x + c*d^2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.207866, size = 18, normalized size = 1.38 \[ \frac{\log \left (e x + d\right )}{c e} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((e*x + d)/(c*e^2*x^2 + 2*c*d*e*x + c*d^2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.128623, size = 12, normalized size = 0.92 \[ \frac{\log{\left (c d + c e x \right )}}{c e} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((e*x+d)/(c*e**2*x**2+2*c*d*e*x+c*d**2),x)
[Out]
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GIAC/XCAS [F(-2)] time = 0., size = 0, normalized size = 0. \[ \text{Exception raised: NotImplementedError} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((e*x + d)/(c*e^2*x^2 + 2*c*d*e*x + c*d^2),x, algorithm="giac")
[Out]