Optimal. Leaf size=25 \[ \frac{2 \left (a x^2+b x^3\right )^{5/2}}{5 b x^5} \]
[Out]
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Rubi [A] time = 0.0671833, antiderivative size = 25, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 19, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.053 \[ \frac{2 \left (a x^2+b x^3\right )^{5/2}}{5 b x^5} \]
Antiderivative was successfully verified.
[In] Int[(a*x^2 + b*x^3)^(3/2)/x^3,x]
[Out]
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Rubi in Sympy [A] time = 7.45821, size = 20, normalized size = 0.8 \[ \frac{2 \left (a x^{2} + b x^{3}\right )^{\frac{5}{2}}}{5 b x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x**3+a*x**2)**(3/2)/x**3,x)
[Out]
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Mathematica [A] time = 0.0215035, size = 23, normalized size = 0.92 \[ \frac{2 \left (x^2 (a+b x)\right )^{5/2}}{5 b x^5} \]
Antiderivative was successfully verified.
[In] Integrate[(a*x^2 + b*x^3)^(3/2)/x^3,x]
[Out]
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Maple [A] time = 0.003, size = 27, normalized size = 1.1 \[{\frac{2\,bx+2\,a}{5\,b{x}^{3}} \left ( b{x}^{3}+a{x}^{2} \right ) ^{{\frac{3}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x^3+a*x^2)^(3/2)/x^3,x)
[Out]
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Maxima [A] time = 1.51756, size = 38, normalized size = 1.52 \[ \frac{2 \,{\left (b^{2} x^{2} + 2 \, a b x + a^{2}\right )} \sqrt{b x + a}}{5 \, b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3 + a*x^2)^(3/2)/x^3,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.22818, size = 50, normalized size = 2. \[ \frac{2 \,{\left (b^{2} x^{2} + 2 \, a b x + a^{2}\right )} \sqrt{b x^{3} + a x^{2}}}{5 \, b x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3 + a*x^2)^(3/2)/x^3,x, algorithm="fricas")
[Out]
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Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{\left (x^{2} \left (a + b x\right )\right )^{\frac{3}{2}}}{x^{3}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x**3+a*x**2)**(3/2)/x**3,x)
[Out]
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GIAC/XCAS [A] time = 0.221377, size = 70, normalized size = 2.8 \[ -\frac{2 \, a^{\frac{5}{2}}{\rm sign}\left (x\right )}{5 \, b} + \frac{2 \,{\left (5 \,{\left (b x + a\right )}^{\frac{3}{2}} a{\rm sign}\left (x\right ) +{\left (3 \,{\left (b x + a\right )}^{\frac{5}{2}} - 5 \,{\left (b x + a\right )}^{\frac{3}{2}} a\right )}{\rm sign}\left (x\right )\right )}}{15 \, b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3 + a*x^2)^(3/2)/x^3,x, algorithm="giac")
[Out]