3.812 \(\int \frac{1-\sqrt{x}}{1+\sqrt [4]{x}} \, dx\)

Optimal. Leaf size=11 \[ x-\frac{4 x^{5/4}}{5} \]

[Out]

x - (4*x^(5/4))/5

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Rubi [A]  time = 0.00621247, antiderivative size = 11, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 19, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.053 \[ x-\frac{4 x^{5/4}}{5} \]

Antiderivative was successfully verified.

[In]  Int[(1 - Sqrt[x])/(1 + x^(1/4)),x]

[Out]

x - (4*x^(5/4))/5

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Rubi in Sympy [A]  time = 1.19604, size = 8, normalized size = 0.73 \[ - \frac{4 x^{\frac{5}{4}}}{5} + x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((1-x**(1/2))/(1+x**(1/4)),x)

[Out]

-4*x**(5/4)/5 + x

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Mathematica [A]  time = 0.000650205, size = 11, normalized size = 1. \[ x-\frac{4 x^{5/4}}{5} \]

Antiderivative was successfully verified.

[In]  Integrate[(1 - Sqrt[x])/(1 + x^(1/4)),x]

[Out]

x - (4*x^(5/4))/5

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Maple [C]  time = 0.013, size = 46, normalized size = 4.2 \[ -{\frac{4}{5}{x}^{{\frac{5}{4}}}}+x+2\,\ln \left ( 1+\sqrt [4]{x} \right ) -\ln \left ( 1-x \right ) -\ln \left ( -1+\sqrt{x} \right ) +\ln \left ( 1+\sqrt{x} \right ) +2\,\ln \left ( \sqrt [4]{x}-1 \right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((1-x^(1/2))/(1+x^(1/4)),x)

[Out]

-4/5*x^(5/4)+x+2*ln(1+x^(1/4))-ln(1-x)-ln(-1+x^(1/2))+ln(1+x^(1/2))+2*ln(x^(1/4)
-1)

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Maxima [A]  time = 0.705103, size = 9, normalized size = 0.82 \[ -\frac{4}{5} \, x^{\frac{5}{4}} + x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-(sqrt(x) - 1)/(x^(1/4) + 1),x, algorithm="maxima")

[Out]

-4/5*x^(5/4) + x

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Fricas [A]  time = 0.267476, size = 9, normalized size = 0.82 \[ -\frac{4}{5} \, x^{\frac{5}{4}} + x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-(sqrt(x) - 1)/(x^(1/4) + 1),x, algorithm="fricas")

[Out]

-4/5*x^(5/4) + x

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Sympy [A]  time = 12.2177, size = 8, normalized size = 0.73 \[ - \frac{4 x^{\frac{5}{4}}}{5} + x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((1-x**(1/2))/(1+x**(1/4)),x)

[Out]

-4*x**(5/4)/5 + x

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GIAC/XCAS [A]  time = 0.265398, size = 9, normalized size = 0.82 \[ -\frac{4}{5} \, x^{\frac{5}{4}} + x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-(sqrt(x) - 1)/(x^(1/4) + 1),x, algorithm="giac")

[Out]

-4/5*x^(5/4) + x