Optimal. Leaf size=26 \[ -\frac{2 b x^{n-3} \sqrt{b x^n}}{3 (2-n)} \]
[Out]
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Rubi [A] time = 0.0166263, antiderivative size = 26, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.154 \[ -\frac{2 b x^{n-3} \sqrt{b x^n}}{3 (2-n)} \]
Antiderivative was successfully verified.
[In] Int[(b*x^n)^(3/2)/x^4,x]
[Out]
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Rubi in Sympy [A] time = 3.22656, size = 31, normalized size = 1.19 \[ - \frac{2 b x^{- \frac{n}{2}} x^{\frac{3 n}{2} - 3} \sqrt{b x^{n}}}{3 \left (- n + 2\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x**n)**(3/2)/x**4,x)
[Out]
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Mathematica [A] time = 0.0103886, size = 22, normalized size = 0.85 \[ \frac{\left (b x^n\right )^{3/2}}{\left (\frac{3 n}{2}-3\right ) x^3} \]
Antiderivative was successfully verified.
[In] Integrate[(b*x^n)^(3/2)/x^4,x]
[Out]
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Maple [A] time = 0.002, size = 18, normalized size = 0.7 \[{\frac{2}{3\,{x}^{3} \left ( -2+n \right ) } \left ( b{x}^{n} \right ) ^{{\frac{3}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x^n)^(3/2)/x^4,x)
[Out]
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Maxima [F] time = 0., size = 0, normalized size = 0. \[ \text{Exception raised: ValueError} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^n)^(3/2)/x^4,x, algorithm="maxima")
[Out]
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Fricas [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^n)^(3/2)/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**n)**(3/2)/x**4,x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{\left (b x^{n}\right )^{\frac{3}{2}}}{x^{4}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^n)^(3/2)/x^4,x, algorithm="giac")
[Out]