3.1023 \(\int \frac{(a+b x)^5}{(a c+b c x)^5} \, dx\)

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

[Out]

x/c^5

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Rubi [A]  time = 0.00588641, antiderivative size = 5, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 18, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.111 \[ \frac{x}{c^5} \]

Antiderivative was successfully verified.

[In]  Int[(a + b*x)^5/(a*c + b*c*x)^5,x]

[Out]

x/c^5

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Rubi in Sympy [A]  time = 3.38393, size = 3, normalized size = 0.6 \[ \frac{x}{c^{5}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((b*x+a)**5/(b*c*x+a*c)**5,x)

[Out]

x/c**5

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Mathematica [A]  time = 0.000455336, size = 5, normalized size = 1. \[ \frac{x}{c^5} \]

Antiderivative was successfully verified.

[In]  Integrate[(a + b*x)^5/(a*c + b*c*x)^5,x]

[Out]

x/c^5

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Maple [A]  time = 0., size = 6, normalized size = 1.2 \[{\frac{x}{{c}^{5}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((b*x+a)^5/(b*c*x+a*c)^5,x)

[Out]

x/c^5

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Maxima [A]  time = 1.33176, size = 7, normalized size = 1.4 \[ \frac{x}{c^{5}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x + a)^5/(b*c*x + a*c)^5,x, algorithm="maxima")

[Out]

x/c^5

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Fricas [A]  time = 0.191484, size = 7, normalized size = 1.4 \[ \frac{x}{c^{5}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x + a)^5/(b*c*x + a*c)^5,x, algorithm="fricas")

[Out]

x/c^5

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Sympy [A]  time = 0.203444, size = 3, normalized size = 0.6 \[ \frac{x}{c^{5}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x+a)**5/(b*c*x+a*c)**5,x)

[Out]

x/c**5

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GIAC/XCAS [A]  time = 0.20925, size = 20, normalized size = 4. \[ \frac{b c x + a c}{b c^{6}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x + a)^5/(b*c*x + a*c)^5,x, algorithm="giac")

[Out]

(b*c*x + a*c)/(b*c^6)