Optimal. Leaf size=35 \[ -\frac{\left (c x^2\right )^p (a+b x)^{2-2 p}}{2 a (1-p) x^2} \]
[Out]
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Rubi [A] time = 0.0309804, antiderivative size = 35, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 22, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.091 \[ -\frac{\left (c x^2\right )^p (a+b x)^{2-2 p}}{2 a (1-p) x^2} \]
Antiderivative was successfully verified.
[In] Int[((c*x^2)^p*(a + b*x)^(1 - 2*p))/x^3,x]
[Out]
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Rubi in Sympy [A] time = 14.6016, size = 36, normalized size = 1.03 \[ - \frac{x^{- 2 p} x^{2 p - 2} \left (c x^{2}\right )^{p} \left (a + b x\right )^{- 2 p + 2}}{2 a \left (- p + 1\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((c*x**2)**p*(b*x+a)**(1-2*p)/x**3,x)
[Out]
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Mathematica [A] time = 0.0442335, size = 33, normalized size = 0.94 \[ \frac{\left (c x^2\right )^p (a+b x)^{2-2 p}}{2 a (p-1) x^2} \]
Antiderivative was successfully verified.
[In] Integrate[((c*x^2)^p*(a + b*x)^(1 - 2*p))/x^3,x]
[Out]
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Maple [A] time = 0.004, size = 32, normalized size = 0.9 \[{\frac{ \left ( bx+a \right ) ^{2-2\,p} \left ( c{x}^{2} \right ) ^{p}}{2\,{x}^{2}a \left ( p-1 \right ) }} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((c*x^2)^p*(b*x+a)^(1-2*p)/x^3,x)
[Out]
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Maxima [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{\left (c x^{2}\right )^{p}{\left (b x + a\right )}^{-2 \, p + 1}}{x^{3}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2)^p*(b*x + a)^(-2*p + 1)/x^3,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.232915, size = 50, normalized size = 1.43 \[ \frac{{\left (b x + a\right )} \left (c x^{2}\right )^{p}{\left (b x + a\right )}^{-2 \, p + 1}}{2 \,{\left (a p - a\right )} x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2)^p*(b*x + a)^(-2*p + 1)/x^3,x, algorithm="fricas")
[Out]
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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**2)**p*(b*x+a)**(1-2*p)/x**3,x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{\left (c x^{2}\right )^{p}{\left (b x + a\right )}^{-2 \, p + 1}}{x^{3}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2)^p*(b*x + a)^(-2*p + 1)/x^3,x, algorithm="giac")
[Out]