Optimal. Leaf size=19 \[ \frac{x (c x)^m}{m \sqrt{b x^2}} \]
[Out]
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Rubi [A] time = 0.0148562, antiderivative size = 19, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 3, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.2 \[ \frac{x (c x)^m}{m \sqrt{b x^2}} \]
Antiderivative was successfully verified.
[In] Int[(c*x)^m/Sqrt[b*x^2],x]
[Out]
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Rubi in Sympy [A] time = 4.2583, size = 17, normalized size = 0.89 \[ \frac{\sqrt{b x^{2}} \left (c x\right )^{m}}{b m x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((c*x)**m/(b*x**2)**(1/2),x)
[Out]
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Mathematica [A] time = 0.00452264, size = 19, normalized size = 1. \[ \frac{x (c x)^m}{m \sqrt{b x^2}} \]
Antiderivative was successfully verified.
[In] Integrate[(c*x)^m/Sqrt[b*x^2],x]
[Out]
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Maple [A] time = 0.004, size = 18, normalized size = 1. \[{\frac{x \left ( cx \right ) ^{m}}{m}{\frac{1}{\sqrt{b{x}^{2}}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((c*x)^m/(b*x^2)^(1/2),x)
[Out]
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Maxima [A] time = 1.46272, size = 18, normalized size = 0.95 \[ \frac{c^{m} x^{m}}{\sqrt{b} m} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x)^m/sqrt(b*x^2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.239581, size = 30, normalized size = 1.58 \[ \frac{\sqrt{b x^{2}} \left (c x\right )^{m}}{b m x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x)^m/sqrt(b*x^2),x, algorithm="fricas")
[Out]
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Sympy [F(-2)] time = 0., size = 0, normalized size = 0. \[ \text{Exception raised: TypeError} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x)**m/(b*x**2)**(1/2),x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{\left (c x\right )^{m}}{\sqrt{b x^{2}}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x)^m/sqrt(b*x^2),x, algorithm="giac")
[Out]