Optimal. Leaf size=12 \[ -\frac{1}{d (c+d x)} \]
[Out]
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Rubi [A] time = 0.0071737, antiderivative size = 12, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 7, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.143 \[ -\frac{1}{d (c+d x)} \]
Antiderivative was successfully verified.
[In] Int[(c + d*x)^(-2),x]
[Out]
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Rubi in Sympy [A] time = 1.28702, size = 8, normalized size = 0.67 \[ - \frac{1}{d \left (c + d x\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(d*x+c)**2,x)
[Out]
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Mathematica [A] time = 0.0037102, size = 12, normalized size = 1. \[ -\frac{1}{d (c+d x)} \]
Antiderivative was successfully verified.
[In] Integrate[(c + d*x)^(-2),x]
[Out]
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Maple [A] time = 0.001, size = 13, normalized size = 1.1 \[ -{\frac{1}{d \left ( dx+c \right ) }} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(d*x+c)^2,x)
[Out]
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Maxima [A] time = 1.3734, size = 16, normalized size = 1.33 \[ -\frac{1}{{\left (d x + c\right )} d} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((d*x + c)^(-2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.197629, size = 18, normalized size = 1.5 \[ -\frac{1}{d^{2} x + c d} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((d*x + c)^(-2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.516234, size = 10, normalized size = 0.83 \[ - \frac{1}{c d + d^{2} x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(d*x+c)**2,x)
[Out]
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GIAC/XCAS [A] time = 0.225863, size = 16, normalized size = 1.33 \[ -\frac{1}{{\left (d x + c\right )} d} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((d*x + c)^(-2),x, algorithm="giac")
[Out]