Optimal. Leaf size=33 \[ \frac{c^2 \sqrt{c x^2} (a+b x)^{n+1}}{b (n+1) x} \]
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Rubi [A] time = 0.0213224, antiderivative size = 33, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.1 \[ \frac{c^2 \sqrt{c x^2} (a+b x)^{n+1}}{b (n+1) x} \]
Antiderivative was successfully verified.
[In] Int[((c*x^2)^(5/2)*(a + b*x)^n)/x^5,x]
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Rubi in Sympy [A] time = 14.949, size = 26, normalized size = 0.79 \[ \frac{c^{2} \sqrt{c x^{2}} \left (a + b x\right )^{n + 1}}{b x \left (n + 1\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((c*x**2)**(5/2)*(b*x+a)**n/x**5,x)
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Mathematica [A] time = 0.0231607, size = 31, normalized size = 0.94 \[ \frac{c^3 x (a+b x)^{n+1}}{b (n+1) \sqrt{c x^2}} \]
Antiderivative was successfully verified.
[In] Integrate[((c*x^2)^(5/2)*(a + b*x)^n)/x^5,x]
[Out]
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Maple [A] time = 0.003, size = 29, normalized size = 0.9 \[{\frac{ \left ( bx+a \right ) ^{1+n}}{b \left ( 1+n \right ){x}^{5}} \left ( c{x}^{2} \right ) ^{{\frac{5}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((c*x^2)^(5/2)*(b*x+a)^n/x^5,x)
[Out]
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Maxima [A] time = 1.36961, size = 38, normalized size = 1.15 \[ \frac{{\left (b c^{\frac{5}{2}} x + a c^{\frac{5}{2}}\right )}{\left (b x + a\right )}^{n}}{b{\left (n + 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2)^(5/2)*(b*x + a)^n/x^5,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.234572, size = 50, normalized size = 1.52 \[ \frac{{\left (b c^{2} x + a c^{2}\right )} \sqrt{c x^{2}}{\left (b x + a\right )}^{n}}{{\left (b n + b\right )} x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2)^(5/2)*(b*x + a)^n/x^5,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)**(5/2)*(b*x+a)**n/x**5,x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{\left (c x^{2}\right )^{\frac{5}{2}}{\left (b x + a\right )}^{n}}{x^{5}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2)^(5/2)*(b*x + a)^n/x^5,x, algorithm="giac")
[Out]