3.2245 \(\int \frac{1+\sqrt{x}}{\sqrt{x}} \, dx\)

Optimal. Leaf size=9 \[ x+2 \sqrt{x} \]

[Out]

2*Sqrt[x] + x

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Rubi [A]  time = 0.0093867, antiderivative size = 9, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.077 \[ x+2 \sqrt{x} \]

Antiderivative was successfully verified.

[In]  Int[(1 + Sqrt[x])/Sqrt[x],x]

[Out]

2*Sqrt[x] + x

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Rubi in Sympy [A]  time = 2.06847, size = 7, normalized size = 0.78 \[ 2 \sqrt{x} + x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((1+x**(1/2))/x**(1/2),x)

[Out]

2*sqrt(x) + x

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Mathematica [A]  time = 0.00242195, size = 9, normalized size = 1. \[ x+2 \sqrt{x} \]

Antiderivative was successfully verified.

[In]  Integrate[(1 + Sqrt[x])/Sqrt[x],x]

[Out]

2*Sqrt[x] + x

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Maple [A]  time = 0.001, size = 8, normalized size = 0.9 \[ x+2\,\sqrt{x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((1+x^(1/2))/x^(1/2),x)

[Out]

x+2*x^(1/2)

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Maxima [A]  time = 1.43398, size = 9, normalized size = 1. \[{\left (\sqrt{x} + 1\right )}^{2} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((sqrt(x) + 1)/sqrt(x),x, algorithm="maxima")

[Out]

(sqrt(x) + 1)^2

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Fricas [A]  time = 0.237127, size = 9, normalized size = 1. \[ x + 2 \, \sqrt{x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((sqrt(x) + 1)/sqrt(x),x, algorithm="fricas")

[Out]

x + 2*sqrt(x)

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Sympy [A]  time = 0.313056, size = 7, normalized size = 0.78 \[ 2 \sqrt{x} + x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((1+x**(1/2))/x**(1/2),x)

[Out]

2*sqrt(x) + x

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GIAC/XCAS [A]  time = 0.214832, size = 9, normalized size = 1. \[ x + 2 \, \sqrt{x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((sqrt(x) + 1)/sqrt(x),x, algorithm="giac")

[Out]

x + 2*sqrt(x)