3.10.53 \(\int (1-\sqrt [4]{x}) \, dx\) [953]

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 = {} \begin {gather*} x-\frac {4 x^{5/4}}{5} \end {gather*}

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 \begin {gather*} x-\frac {4 x^{5/4}}{5} \end {gather*}

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 = 0.02, size = 8, normalized size = 0.73

method	result	size
derivativedivides	\(x -\frac {4 x^{\frac {5}{4}}}{5}\)	\(8\)
default	\(x -\frac {4 x^{\frac {5}{4}}}{5}\)	\(8\)
risch	\(x -\frac {4 x^{\frac {5}{4}}}{5}\)	\(8\)
trager	\(-1+x -\frac {4 x^{\frac {5}{4}}}{5}\)	\(9\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1-x^(1/4),x,method=_RETURNVERBOSE)

[Out]

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

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Maxima [A]
time = 0.26, size = 7, normalized size = 0.64 \begin {gather*} -\frac {4}{5} \, x^{\frac {5}{4}} + x \end {gather*}

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 = 0.33, size = 7, normalized size = 0.64 \begin {gather*} -\frac {4}{5} \, x^{\frac {5}{4}} + x \end {gather*}

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 = 0.01, size = 8, normalized size = 0.73 \begin {gather*} - \frac {4 x^{\frac {5}{4}}}{5} + x \end {gather*}

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 = 3.87, size = 7, normalized size = 0.64 \begin {gather*} -\frac {4}{5} \, x^{\frac {5}{4}} + x \end {gather*}

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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Mupad [B]
time = 0.02, size = 7, normalized size = 0.64 \begin {gather*} x-\frac {4\,x^{5/4}}{5} \end {gather*}

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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