3.953 \(\int (1-\sqrt [4]{x}) \, dx\)

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

[Out]

x-4/5*x^(5/4)

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Rubi [A]  time = 0.00, antiderivative size = 11, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 0, integrand size = 9, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \[ x-\frac {4 x^{5/4}}{5} \]

Antiderivative was successfully verified.

[In]

Int[1 - x^(1/4),x]

[Out]

x - (4*x^(5/4))/5

Rubi steps

\begin {align*} \int \left (1-\sqrt [4]{x}\right ) \, dx &=x-\frac {4 x^{5/4}}{5}\\ \end {align*}

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Mathematica [A]  time = 0.00, size = 11, normalized size = 1.00 \[ x-\frac {4 x^{5/4}}{5} \]

Antiderivative was successfully verified.

[In]

Integrate[1 - x^(1/4),x]

[Out]

x - (4*x^(5/4))/5

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fricas [A]  time = 1.28, size = 7, normalized size = 0.64 \[ -\frac {4}{5} \, x^{\frac {5}{4}} + x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1-x^(1/4),x, algorithm="fricas")

[Out]

-4/5*x^(5/4) + x

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giac [A]  time = 0.35, size = 7, normalized size = 0.64 \[ -\frac {4}{5} \, x^{\frac {5}{4}} + x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1-x^(1/4),x, algorithm="giac")

[Out]

-4/5*x^(5/4) + x

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maple [A]  time = 0.00, 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]

int(1-x^(1/4),x)

[Out]

x-4/5*x^(5/4)

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maxima [A]  time = 0.62, size = 7, normalized size = 0.64 \[ -\frac {4}{5} \, x^{\frac {5}{4}} + x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1-x^(1/4),x, algorithm="maxima")

[Out]

-4/5*x^(5/4) + x

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mupad [B]  time = 0.02, size = 7, normalized size = 0.64 \[ x-\frac {4\,x^{5/4}}{5} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1 - x^(1/4),x)

[Out]

x - (4*x^(5/4))/5

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sympy [A]  time = 0.06, 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**(1/4),x)

[Out]

-4*x**(5/4)/5 + x

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