Optimal. Leaf size=36 \[ \frac{2 x^{1-n} (c x)^m}{b (2 m-3 n+2) \sqrt{b x^n}} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0212993, antiderivative size = 36, 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 \[ \frac{2 x^{1-n} (c x)^m}{b (2 m-3 n+2) \sqrt{b x^n}} \]
Antiderivative was successfully verified.
[In] Int[(c*x)^m/(b*x^n)^(3/2),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 6.05171, size = 44, normalized size = 1.22 \[ \frac{2 x^{- m} x^{- \frac{n}{2}} x^{m - \frac{3 n}{2} + 1} \sqrt{b x^{n}} \left (c x\right )^{m}}{b^{2} \left (2 m - 3 n + 2\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((c*x)**m/(b*x**n)**(3/2),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0119936, size = 26, normalized size = 0.72 \[ \frac{x (c x)^m}{\left (m-\frac{3 n}{2}+1\right ) \left (b x^n\right )^{3/2}} \]
Antiderivative was successfully verified.
[In] Integrate[(c*x)^m/(b*x^n)^(3/2),x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.001, size = 26, normalized size = 0.7 \[ 2\,{\frac{x \left ( cx \right ) ^{m}}{ \left ( 2+2\,m-3\,n \right ) \left ( b{x}^{n} \right ) ^{3/2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((c*x)^m/(b*x^n)^(3/2),x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.45976, size = 36, normalized size = 1. \[ \frac{2 \, c^{m} x x^{m}}{b^{\frac{3}{2}}{\left (2 \, m - 3 \, n + 2\right )}{\left (x^{n}\right )}^{\frac{3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x)^m/(b*x^n)^(3/2),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
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((c*x)^m/(b*x^n)^(3/2),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [F(-1)] time = 0., size = 0, normalized size = 0. \[ \text{Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x)**m/(b*x**n)**(3/2),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{\left (c x\right )^{m}}{\left (b x^{n}\right )^{\frac{3}{2}}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x)^m/(b*x^n)^(3/2),x, algorithm="giac")
[Out]