Optimal. Leaf size=30 \[ \frac{1}{4} e \log (2 x+3)-\frac{2 d-3 e}{4 (2 x+3)} \]
[Out]
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Rubi [A] time = 0.0458462, antiderivative size = 30, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 18, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.111 \[ \frac{1}{4} e \log (2 x+3)-\frac{2 d-3 e}{4 (2 x+3)} \]
Antiderivative was successfully verified.
[In] Int[(d + e*x)/(9 + 12*x + 4*x^2),x]
[Out]
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Rubi in Sympy [A] time = 9.35401, size = 22, normalized size = 0.73 \[ \frac{e \log{\left (2 x + 3 \right )}}{4} - \frac{\frac{d}{2} - \frac{3 e}{4}}{2 x + 3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((e*x+d)/(4*x**2+12*x+9),x)
[Out]
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Mathematica [A] time = 0.012, size = 30, normalized size = 1. \[ \frac{3 e-2 d}{4 (2 x+3)}+\frac{1}{4} e \log (2 x+3) \]
Antiderivative was successfully verified.
[In] Integrate[(d + e*x)/(9 + 12*x + 4*x^2),x]
[Out]
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Maple [A] time = 0.009, size = 31, normalized size = 1. \[{\frac{e\ln \left ( 2\,x+3 \right ) }{4}}-{\frac{d}{4\,x+6}}+{\frac{3\,e}{8\,x+12}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((e*x+d)/(4*x^2+12*x+9),x)
[Out]
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Maxima [A] time = 0.682783, size = 35, normalized size = 1.17 \[ \frac{1}{4} \, e \log \left (2 \, x + 3\right ) - \frac{2 \, d - 3 \, e}{4 \,{\left (2 \, x + 3\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((e*x + d)/(4*x^2 + 12*x + 9),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.19939, size = 42, normalized size = 1.4 \[ \frac{{\left (2 \, e x + 3 \, e\right )} \log \left (2 \, x + 3\right ) - 2 \, d + 3 \, e}{4 \,{\left (2 \, x + 3\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((e*x + d)/(4*x^2 + 12*x + 9),x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.18805, size = 20, normalized size = 0.67 \[ \frac{e \log{\left (2 x + 3 \right )}}{4} - \frac{2 d - 3 e}{8 x + 12} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((e*x+d)/(4*x**2+12*x+9),x)
[Out]
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GIAC/XCAS [A] time = 0.211599, size = 39, normalized size = 1.3 \[ \frac{1}{4} \, e{\rm ln}\left ({\left | 2 \, x + 3 \right |}\right ) - \frac{2 \, d - 3 \, e}{4 \,{\left (2 \, x + 3\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((e*x + d)/(4*x^2 + 12*x + 9),x, algorithm="giac")
[Out]