Optimal. Leaf size=28 \[ -\frac{2 c \sqrt{\frac{c}{(a+b x)^3}}}{7 b (a+b x)^2} \]
[Out]
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Rubi [A] time = 0.0248742, antiderivative size = 28, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 3, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.231 \[ -\frac{2 c \sqrt{\frac{c}{(a+b x)^3}}}{7 b (a+b x)^2} \]
Antiderivative was successfully verified.
[In] Int[(c/(a + b*x)^3)^(3/2),x]
[Out]
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Rubi in Sympy [A] time = 2.09856, size = 26, normalized size = 0.93 \[ - \frac{2 c \sqrt{\frac{c}{\left (a + b x\right )^{3}}}}{7 b \left (a + b x\right )^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((c/(b*x+a)**3)**(3/2),x)
[Out]
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Mathematica [A] time = 0.0145915, size = 25, normalized size = 0.89 \[ -\frac{2 (a+b x) \left (\frac{c}{(a+b x)^3}\right )^{3/2}}{7 b} \]
Antiderivative was successfully verified.
[In] Integrate[(c/(a + b*x)^3)^(3/2),x]
[Out]
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Maple [A] time = 0.002, size = 22, normalized size = 0.8 \[ -{\frac{2\,bx+2\,a}{7\,b} \left ({\frac{c}{ \left ( bx+a \right ) ^{3}}} \right ) ^{{\frac{3}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((c/(b*x+a)^3)^(3/2),x)
[Out]
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Maxima [A] time = 1.47643, size = 32, normalized size = 1.14 \[ -\frac{2 \,{\left (b c^{\frac{3}{2}} x + a c^{\frac{3}{2}}\right )}}{7 \,{\left (b x + a\right )}^{\frac{9}{2}} b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c/(b*x + a)^3)^(3/2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.218368, size = 78, normalized size = 2.79 \[ -\frac{2 \, c \sqrt{\frac{c}{b^{3} x^{3} + 3 \, a b^{2} x^{2} + 3 \, a^{2} b x + a^{3}}}}{7 \,{\left (b^{3} x^{2} + 2 \, a b^{2} x + a^{2} b\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c/(b*x + a)^3)^(3/2),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/(b*x+a)**3)**(3/2),x)
[Out]
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GIAC/XCAS [A] time = 0.221549, size = 70, normalized size = 2.5 \[ -\frac{2 \, c^{5}{\rm sign}\left (b^{3} x^{3} + 3 \, a b^{2} x^{2} + 3 \, a^{2} b x + a^{3}\right ){\rm sign}\left (b x + a\right )}{7 \,{\left (b c x + a c\right )}^{\frac{7}{2}} b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c/(b*x + a)^3)^(3/2),x, algorithm="giac")
[Out]