Optimal. Leaf size=16 \[ \frac{2 (c+d x)^{3/2}}{3 d} \]
[Out]
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Rubi [A] time = 0.00717338, antiderivative size = 16, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 9, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.111 \[ \frac{2 (c+d x)^{3/2}}{3 d} \]
Antiderivative was successfully verified.
[In] Int[Sqrt[c + d*x],x]
[Out]
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Rubi in Sympy [A] time = 1.37057, size = 12, normalized size = 0.75 \[ \frac{2 \left (c + d x\right )^{\frac{3}{2}}}{3 d} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((d*x+c)**(1/2),x)
[Out]
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Mathematica [A] time = 0.00524516, size = 16, normalized size = 1. \[ \frac{2 (c+d x)^{3/2}}{3 d} \]
Antiderivative was successfully verified.
[In] Integrate[Sqrt[c + d*x],x]
[Out]
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Maple [A] time = 0.003, size = 13, normalized size = 0.8 \[{\frac{2}{3\,d} \left ( dx+c \right ) ^{{\frac{3}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((d*x+c)^(1/2),x)
[Out]
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Maxima [A] time = 1.33734, size = 16, normalized size = 1. \[ \frac{2 \,{\left (d x + c\right )}^{\frac{3}{2}}}{3 \, d} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(d*x + c),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.208801, size = 16, normalized size = 1. \[ \frac{2 \,{\left (d x + c\right )}^{\frac{3}{2}}}{3 \, d} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(d*x + c),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.033368, size = 12, normalized size = 0.75 \[ \frac{2 \left (c + d x\right )^{\frac{3}{2}}}{3 d} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((d*x+c)**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.214285, size = 16, normalized size = 1. \[ \frac{2 \,{\left (d x + c\right )}^{\frac{3}{2}}}{3 \, d} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(d*x + c),x, algorithm="giac")
[Out]