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

Optimal. Leaf size=9 \[ 2 \sqrt{x+1} \]

[Out]

2*Sqrt[1 + x]

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Rubi [A]  time = 0.00440617, antiderivative size = 9, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 7, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.143 \[ 2 \sqrt{x+1} \]

Antiderivative was successfully verified.

[In]  Int[1/Sqrt[1 + x],x]

[Out]

2*Sqrt[1 + x]

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Rubi in Sympy [A]  time = 0.522944, size = 7, normalized size = 0.78 \[ 2 \sqrt{x + 1} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

2*sqrt(x + 1)

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Mathematica [A]  time = 0.00155672, size = 9, normalized size = 1. \[ 2 \sqrt{x+1} \]

Antiderivative was successfully verified.

[In]  Integrate[1/Sqrt[1 + x],x]

[Out]

2*Sqrt[1 + x]

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Maple [A]  time = 0.003, size = 8, normalized size = 0.9 \[ 2\,\sqrt{1+x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(1/(1+x)^(1/2),x)

[Out]

2*(1+x)^(1/2)

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Maxima [A]  time = 0.682816, size = 9, normalized size = 1. \[ 2 \, \sqrt{x + 1} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

2*sqrt(x + 1)

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Fricas [A]  time = 0.259293, size = 9, normalized size = 1. \[ 2 \, \sqrt{x + 1} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

2*sqrt(x + 1)

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Sympy [A]  time = 0.06467, size = 7, normalized size = 0.78 \[ 2 \sqrt{x + 1} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(1/(1+x)**(1/2),x)

[Out]

2*sqrt(x + 1)

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GIAC/XCAS [A]  time = 0.265011, size = 9, normalized size = 1. \[ 2 \, \sqrt{x + 1} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

2*sqrt(x + 1)