Optimal. Leaf size=19 \[ -\frac{\left (b x^2\right )^p}{(3-2 p) x^3} \]
[Out]
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Rubi [A] time = 0.0159492, antiderivative size = 19, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.182 \[ -\frac{\left (b x^2\right )^p}{(3-2 p) x^3} \]
Antiderivative was successfully verified.
[In] Int[(b*x^2)^p/x^4,x]
[Out]
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Rubi in Sympy [A] time = 3.03222, size = 24, normalized size = 1.26 \[ - \frac{x^{- 2 p} x^{2 p - 3} \left (b x^{2}\right )^{p}}{- 2 p + 3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x**2)**p/x**4,x)
[Out]
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Mathematica [A] time = 0.00373292, size = 18, normalized size = 0.95 \[ \frac{\left (b x^2\right )^p}{(2 p-3) x^3} \]
Antiderivative was successfully verified.
[In] Integrate[(b*x^2)^p/x^4,x]
[Out]
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Maple [A] time = 0.002, size = 19, normalized size = 1. \[{\frac{ \left ( b{x}^{2} \right ) ^{p}}{{x}^{3} \left ( 2\,p-3 \right ) }} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x^2)^p/x^4,x)
[Out]
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Maxima [A] time = 1.45182, size = 26, normalized size = 1.37 \[ \frac{b^{p} x^{2 \, p}}{{\left (2 \, p - 3\right )} x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^2)^p/x^4,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.236238, size = 24, normalized size = 1.26 \[ \frac{\left (b x^{2}\right )^{p}}{{\left (2 \, p - 3\right )} x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^2)^p/x^4,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((b*x**2)**p/x**4,x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{\left (b x^{2}\right )^{p}}{x^{4}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^2)^p/x^4,x, algorithm="giac")
[Out]