Optimal. Leaf size=18 \[ \frac{a x}{c^4}+\frac{b x^2}{2 c^4} \]
[Out]
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Rubi [A] time = 0.0129734, antiderivative size = 18, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 18, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.056 \[ \frac{a x}{c^4}+\frac{b x^2}{2 c^4} \]
Antiderivative was successfully verified.
[In] Int[(a + b*x)^5/(a*c + b*c*x)^4,x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ \frac{b \int x\, dx}{c^{4}} + \frac{\int a\, dx}{c^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x+a)**5/(b*c*x+a*c)**4,x)
[Out]
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Mathematica [A] time = 0.00101563, size = 16, normalized size = 0.89 \[ \frac{a x+\frac{b x^2}{2}}{c^4} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x)^5/(a*c + b*c*x)^4,x]
[Out]
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Maple [A] time = 0., size = 15, normalized size = 0.8 \[{\frac{1}{{c}^{4}} \left ( ax+{\frac{b{x}^{2}}{2}} \right ) } \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x+a)^5/(b*c*x+a*c)^4,x)
[Out]
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Maxima [A] time = 1.32772, size = 20, normalized size = 1.11 \[ \frac{b x^{2} + 2 \, a x}{2 \, c^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)^5/(b*c*x + a*c)^4,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.191292, size = 20, normalized size = 1.11 \[ \frac{b x^{2} + 2 \, a x}{2 \, c^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)^5/(b*c*x + a*c)^4,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.202368, size = 15, normalized size = 0.83 \[ \frac{a x}{c^{4}} + \frac{b x^{2}}{2 c^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x+a)**5/(b*c*x+a*c)**4,x)
[Out]
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GIAC/XCAS [A] time = 0.208434, size = 28, normalized size = 1.56 \[ \frac{b c^{4} x^{2} + 2 \, a c^{4} x}{2 \, c^{8}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)^5/(b*c*x + a*c)^4,x, algorithm="giac")
[Out]