Optimal. Leaf size=20 \[ \frac{2 \sqrt{a c+b c x}}{b c^6} \]
[Out]
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Rubi [A] time = 0.0132467, antiderivative size = 20, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.1 \[ \frac{2 \sqrt{a c+b c x}}{b c^6} \]
Antiderivative was successfully verified.
[In] Int[(a + b*x)^5/(a*c + b*c*x)^(11/2),x]
[Out]
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Rubi in Sympy [A] time = 4.29449, size = 17, normalized size = 0.85 \[ \frac{2 \sqrt{a c + b c x}}{b c^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x+a)**5/(b*c*x+a*c)**(11/2),x)
[Out]
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Mathematica [A] time = 0.0120304, size = 24, normalized size = 1.2 \[ \frac{2 (a+b x)}{b c^5 \sqrt{c (a+b x)}} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x)^5/(a*c + b*c*x)^(11/2),x]
[Out]
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Maple [A] time = 0.005, size = 23, normalized size = 1.2 \[ 2\,{\frac{ \left ( bx+a \right ) ^{6}}{b \left ( bcx+ac \right ) ^{11/2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x+a)^5/(b*c*x+a*c)^(11/2),x)
[Out]
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Maxima [A] time = 1.33905, size = 24, normalized size = 1.2 \[ \frac{2 \, \sqrt{b c x + a c}}{b c^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)^5/(b*c*x + a*c)^(11/2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.205514, size = 24, normalized size = 1.2 \[ \frac{2 \, \sqrt{b c x + a c}}{b c^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)^5/(b*c*x + a*c)^(11/2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 22.1551, size = 29, normalized size = 1.45 \[ \begin{cases} \frac{2 \sqrt{a c + b c x}}{b c^{6}} & \text{for}\: b \neq 0 \\\frac{a^{5} x}{\left (a c\right )^{\frac{11}{2}}} & \text{otherwise} \end{cases} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x+a)**5/(b*c*x+a*c)**(11/2),x)
[Out]
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GIAC/XCAS [A] time = 0.226985, size = 24, normalized size = 1.2 \[ \frac{2 \, \sqrt{b c x + a c}}{b c^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)^5/(b*c*x + a*c)^(11/2),x, algorithm="giac")
[Out]