Optimal. Leaf size=31 \[ -\frac{2 d-3 e}{12 (2 x+3)^3}-\frac{e}{8 (2 x+3)^2} \]
[Out]
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Rubi [A] time = 0.0443564, antiderivative size = 31, 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 \[ -\frac{2 d-3 e}{12 (2 x+3)^3}-\frac{e}{8 (2 x+3)^2} \]
Antiderivative was successfully verified.
[In] Int[(d + e*x)/(9 + 12*x + 4*x^2)^2,x]
[Out]
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Rubi in Sympy [A] time = 9.70317, size = 24, normalized size = 0.77 \[ - \frac{e}{8 \left (2 x + 3\right )^{2}} - \frac{\frac{d}{6} - \frac{e}{4}}{\left (2 x + 3\right )^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((e*x+d)/(4*x**2+12*x+9)**2,x)
[Out]
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Mathematica [A] time = 0.0131996, size = 22, normalized size = 0.71 \[ -\frac{4 d+6 e x+3 e}{24 (2 x+3)^3} \]
Antiderivative was successfully verified.
[In] Integrate[(d + e*x)/(9 + 12*x + 4*x^2)^2,x]
[Out]
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Maple [A] time = 0.008, size = 28, normalized size = 0.9 \[ -{\frac{e}{8\, \left ( 2\,x+3 \right ) ^{2}}}-{\frac{1}{3\, \left ( 2\,x+3 \right ) ^{3}} \left ({\frac{d}{2}}-{\frac{3\,e}{4}} \right ) } \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((e*x+d)/(4*x^2+12*x+9)^2,x)
[Out]
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Maxima [A] time = 0.691078, size = 41, normalized size = 1.32 \[ -\frac{6 \, e x + 4 \, d + 3 \, e}{24 \,{\left (8 \, x^{3} + 36 \, x^{2} + 54 \, x + 27\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((e*x + d)/(4*x^2 + 12*x + 9)^2,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.19663, size = 41, normalized size = 1.32 \[ -\frac{6 \, e x + 4 \, d + 3 \, e}{24 \,{\left (8 \, x^{3} + 36 \, x^{2} + 54 \, x + 27\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((e*x + d)/(4*x^2 + 12*x + 9)^2,x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.4651, size = 27, normalized size = 0.87 \[ - \frac{4 d + 6 e x + 3 e}{192 x^{3} + 864 x^{2} + 1296 x + 648} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((e*x+d)/(4*x**2+12*x+9)**2,x)
[Out]
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GIAC/XCAS [A] time = 0.207897, size = 30, normalized size = 0.97 \[ -\frac{6 \, x e + 4 \, d + 3 \, e}{24 \,{\left (2 \, x + 3\right )}^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((e*x + d)/(4*x^2 + 12*x + 9)^2,x, algorithm="giac")
[Out]