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

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 = 0.0012273, antiderivative size = 11, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 0, integrand size = 9, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0., 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*}

Mathematica [A]  time = 0.0015435, size = 11, normalized size = 1. \[ x-\frac{4 x^{5/4}}{5} \]

Antiderivative was successfully verified.

[In]

Integrate[1 - x^(1/4),x]

[Out]

x - (4*x^(5/4))/5

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Maple [A]  time = 0., size = 8, normalized size = 0.7 \begin{align*} x-{\frac{4}{5}{x}^{{\frac{5}{4}}}} \end{align*}

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 = 1.00362, size = 9, normalized size = 0.82 \begin{align*} -\frac{4}{5} \, x^{\frac{5}{4}} + x \end{align*}

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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Fricas [A]  time = 1.48727, size = 24, normalized size = 2.18 \begin{align*} -\frac{4}{5} \, x^{\frac{5}{4}} + x \end{align*}

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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Sympy [A]  time = 0.053714, size = 8, normalized size = 0.73 \begin{align*} - \frac{4 x^{\frac{5}{4}}}{5} + x \end{align*}

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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Giac [A]  time = 1.12614, size = 9, normalized size = 0.82 \begin{align*} -\frac{4}{5} \, x^{\frac{5}{4}} + x \end{align*}

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