Optimal. Leaf size=25 \[ \frac{2 (a+b x) \sqrt{c (a+b x)^3}}{5 b} \]
[Out]
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Rubi [A] time = 0.029352, antiderivative size = 25, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 3, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.231 \[ \frac{2 (a+b x) \sqrt{c (a+b x)^3}}{5 b} \]
Antiderivative was successfully verified.
[In] Int[Sqrt[c*(a + b*x)^3],x]
[Out]
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Rubi in Sympy [A] time = 9.29164, size = 51, normalized size = 2.04 \[ \frac{2 \left (3 a + 3 b x\right ) \sqrt{a^{3} c + 3 a^{2} b c x + 3 a b^{2} c x^{2} + b^{3} c x^{3}}}{15 b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((c*(b*x+a)**3)**(1/2),x)
[Out]
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Mathematica [A] time = 0.0114887, size = 25, normalized size = 1. \[ \frac{2 (a+b x) \sqrt{c (a+b x)^3}}{5 b} \]
Antiderivative was successfully verified.
[In] Integrate[Sqrt[c*(a + b*x)^3],x]
[Out]
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Maple [A] time = 0.004, size = 22, normalized size = 0.9 \[{\frac{2\,bx+2\,a}{5\,b}\sqrt{c \left ( bx+a \right ) ^{3}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((c*(b*x+a)^3)^(1/2),x)
[Out]
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Maxima [A] time = 1.39501, size = 32, normalized size = 1.28 \[ \frac{2 \,{\left (b \sqrt{c} x + a \sqrt{c}\right )}{\left (b x + a\right )}^{\frac{3}{2}}}{5 \, b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt((b*x + a)^3*c),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.214091, size = 59, normalized size = 2.36 \[ \frac{2 \, \sqrt{b^{3} c x^{3} + 3 \, a b^{2} c x^{2} + 3 \, a^{2} b c x + a^{3} c}{\left (b x + a\right )}}{5 \, b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt((b*x + a)^3*c),x, algorithm="fricas")
[Out]
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Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \sqrt{c \left (a + b x\right )^{3}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*(b*x+a)**3)**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.219801, size = 89, normalized size = 3.56 \[ \frac{2 \,{\left (5 \,{\left (b c x + a c\right )}^{\frac{3}{2}} a{\rm sign}\left (b x + a\right ) - \frac{{\left (5 \,{\left (b c x + a c\right )}^{\frac{3}{2}} a c - 3 \,{\left (b c x + a c\right )}^{\frac{5}{2}}\right )}{\rm sign}\left (b x + a\right )}{c}\right )}}{15 \, b c} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt((b*x + a)^3*c),x, algorithm="giac")
[Out]