3.1009 \(\int \frac{(d+e x)^6}{\left (c d^2+2 c d e x+c e^2 x^2\right )^3} \, dx\)

Optimal. Leaf size=5 \[ \frac{x}{c^3} \]

[Out]

x/c^3

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Rubi [A]  time = 0.00975084, antiderivative size = 5, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 30, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.067 \[ \frac{x}{c^3} \]

Antiderivative was successfully verified.

[In]  Int[(d + e*x)^6/(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^3,x]

[Out]

x/c^3

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Rubi in Sympy [A]  time = 16.625, size = 3, normalized size = 0.6 \[ \frac{x}{c^{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((e*x+d)**6/(c*e**2*x**2+2*c*d*e*x+c*d**2)**3,x)

[Out]

x/c**3

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Mathematica [A]  time = 0.000768919, size = 5, normalized size = 1. \[ \frac{x}{c^3} \]

Antiderivative was successfully verified.

[In]  Integrate[(d + e*x)^6/(c*d^2 + 2*c*d*e*x + c*e^2*x^2)^3,x]

[Out]

x/c^3

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Maple [A]  time = 0., size = 6, normalized size = 1.2 \[{\frac{x}{{c}^{3}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((e*x+d)^6/(c*e^2*x^2+2*c*d*e*x+c*d^2)^3,x)

[Out]

x/c^3

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Maxima [A]  time = 0.694819, size = 7, normalized size = 1.4 \[ \frac{x}{c^{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((e*x + d)^6/(c*e^2*x^2 + 2*c*d*e*x + c*d^2)^3,x, algorithm="maxima")

[Out]

x/c^3

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Fricas [A]  time = 0.214832, size = 7, normalized size = 1.4 \[ \frac{x}{c^{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((e*x + d)^6/(c*e^2*x^2 + 2*c*d*e*x + c*d^2)^3,x, algorithm="fricas")

[Out]

x/c^3

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Sympy [A]  time = 0.230588, size = 3, normalized size = 0.6 \[ \frac{x}{c^{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((e*x+d)**6/(c*e**2*x**2+2*c*d*e*x+c*d**2)**3,x)

[Out]

x/c**3

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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)^6/(c*e^2*x^2 + 2*c*d*e*x + c*d^2)^3,x, algorithm="giac")

[Out]

Exception raised: NotImplementedError