Optimal. Leaf size=37 \[ \frac{1}{4} a c x^3 \sqrt{c x^2}+\frac{1}{5} b c x^4 \sqrt{c x^2} \]
[Out]
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Rubi [A] time = 0.0254089, antiderivative size = 37, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.133 \[ \frac{1}{4} a c x^3 \sqrt{c x^2}+\frac{1}{5} b c x^4 \sqrt{c x^2} \]
Antiderivative was successfully verified.
[In] Int[(c*x^2)^(3/2)*(a + b*x),x]
[Out]
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Rubi in Sympy [A] time = 5.60317, size = 32, normalized size = 0.86 \[ \frac{a c x^{3} \sqrt{c x^{2}}}{4} + \frac{b c x^{4} \sqrt{c x^{2}}}{5} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((c*x**2)**(3/2)*(b*x+a),x)
[Out]
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Mathematica [A] time = 0.00726745, size = 22, normalized size = 0.59 \[ \frac{1}{20} x \left (c x^2\right )^{3/2} (5 a+4 b x) \]
Antiderivative was successfully verified.
[In] Integrate[(c*x^2)^(3/2)*(a + b*x),x]
[Out]
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Maple [A] time = 0.005, size = 19, normalized size = 0.5 \[{\frac{x \left ( 4\,bx+5\,a \right ) }{20} \left ( c{x}^{2} \right ) ^{{\frac{3}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((c*x^2)^(3/2)*(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)^(3/2)*(b*x + a),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.204298, size = 32, normalized size = 0.86 \[ \frac{1}{20} \,{\left (4 \, b c x^{4} + 5 \, a c x^{3}\right )} \sqrt{c x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2)^(3/2)*(b*x + a),x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.59594, size = 34, normalized size = 0.92 \[ \frac{a c^{\frac{3}{2}} x \left (x^{2}\right )^{\frac{3}{2}}}{4} + \frac{b c^{\frac{3}{2}} x^{2} \left (x^{2}\right )^{\frac{3}{2}}}{5} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x**2)**(3/2)*(b*x+a),x)
[Out]
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GIAC/XCAS [A] time = 0.205249, size = 30, normalized size = 0.81 \[ \frac{1}{20} \,{\left (4 \, b x^{5}{\rm sign}\left (x\right ) + 5 \, a x^{4}{\rm sign}\left (x\right )\right )} c^{\frac{3}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2)^(3/2)*(b*x + a),x, algorithm="giac")
[Out]