Optimal. Leaf size=41 \[ \frac{1}{7} a c^2 x^6 \sqrt{c x^2}+\frac{1}{8} b c^2 x^7 \sqrt{c x^2} \]
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Rubi [A] time = 0.030822, antiderivative size = 41, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 16, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.125 \[ \frac{1}{7} a c^2 x^6 \sqrt{c x^2}+\frac{1}{8} b c^2 x^7 \sqrt{c x^2} \]
Antiderivative was successfully verified.
[In] Int[x*(c*x^2)^(5/2)*(a + b*x),x]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int x \left (c x^{2}\right )^{\frac{5}{2}} \left (a + b x\right )\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x*(c*x**2)**(5/2)*(b*x+a),x)
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Mathematica [A] time = 0.00945454, size = 24, normalized size = 0.59 \[ \frac{1}{56} x^2 \left (c x^2\right )^{5/2} (8 a+7 b x) \]
Antiderivative was successfully verified.
[In] Integrate[x*(c*x^2)^(5/2)*(a + b*x),x]
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Maple [A] time = 0.005, size = 21, normalized size = 0.5 \[{\frac{{x}^{2} \left ( 7\,bx+8\,a \right ) }{56} \left ( c{x}^{2} \right ) ^{{\frac{5}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x*(c*x^2)^(5/2)*(b*x+a),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((c*x^2)^(5/2)*(b*x + a)*x,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.208879, size = 38, normalized size = 0.93 \[ \frac{1}{56} \,{\left (7 \, b c^{2} x^{7} + 8 \, a c^{2} x^{6}\right )} \sqrt{c x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2)^(5/2)*(b*x + a)*x,x, algorithm="fricas")
[Out]
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Sympy [A] time = 6.39168, size = 36, normalized size = 0.88 \[ \frac{a c^{\frac{5}{2}} x^{2} \left (x^{2}\right )^{\frac{5}{2}}}{7} + \frac{b c^{\frac{5}{2}} x^{3} \left (x^{2}\right )^{\frac{5}{2}}}{8} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x*(c*x**2)**(5/2)*(b*x+a),x)
[Out]
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GIAC/XCAS [A] time = 0.20429, size = 38, normalized size = 0.93 \[ \frac{1}{56} \,{\left (7 \, b c^{2} x^{8}{\rm sign}\left (x\right ) + 8 \, a c^{2} x^{7}{\rm sign}\left (x\right )\right )} \sqrt{c} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2)^(5/2)*(b*x + a)*x,x, algorithm="giac")
[Out]