3.20.11 \(\int (33+\sqrt [33]{x}) \, dx\) [1911]

Optimal. Leaf size=13 \[ 33 x+\frac {33 x^{34/33}}{34} \]

[Out]

33*x+33/34*x^(34/33)

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Rubi [A]
time = 0.00, antiderivative size = 13, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 0, integrand size = 7, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \frac {33 x^{34/33}}{34}+33 x \end {gather*}

Antiderivative was successfully verified.

[In]

Int[33 + x^(1/33),x]

[Out]

33*x + (33*x^(34/33))/34

Rubi steps

\begin {align*} \int \left (33+\sqrt [33]{x}\right ) \, dx &=33 x+\frac {33 x^{34/33}}{34}\\ \end {align*}

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Mathematica [A]
time = 0.00, size = 13, normalized size = 1.00 \begin {gather*} 33 x+\frac {33 x^{34/33}}{34} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[33 + x^(1/33),x]

[Out]

33*x + (33*x^(34/33))/34

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Maple [A]
time = 0.17, size = 10, normalized size = 0.77

method	result	size
derivativedivides	\(33 x +\frac {33 x^{\frac {34}{33}}}{34}\)	\(10\)
default	\(33 x +\frac {33 x^{\frac {34}{33}}}{34}\)	\(10\)
risch	\(33 x +\frac {33 x^{\frac {34}{33}}}{34}\)	\(10\)
trager	\(-33+33 x +\frac {33 x^{\frac {34}{33}}}{34}\)	\(11\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(33+x^(1/33),x,method=_RETURNVERBOSE)

[Out]

33*x+33/34*x^(34/33)

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Maxima [A]
time = 0.26, size = 9, normalized size = 0.69 \begin {gather*} \frac {33}{34} \, x^{\frac {34}{33}} + 33 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(33+x^(1/33),x, algorithm="maxima")

[Out]

33/34*x^(34/33) + 33*x

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Fricas [A]
time = 0.91, size = 9, normalized size = 0.69 \begin {gather*} \frac {33}{34} \, x^{\frac {34}{33}} + 33 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(33+x^(1/33),x, algorithm="fricas")

[Out]

33/34*x^(34/33) + 33*x

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Sympy [A]
time = 0.01, size = 10, normalized size = 0.77 \begin {gather*} \frac {33 x^{\frac {34}{33}}}{34} + 33 x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(33+x**(1/33),x)

[Out]

33*x**(34/33)/34 + 33*x

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Giac [A]
time = 1.35, size = 9, normalized size = 0.69 \begin {gather*} \frac {33}{34} \, x^{\frac {34}{33}} + 33 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(33+x^(1/33),x, algorithm="giac")

[Out]

33/34*x^(34/33) + 33*x

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Mupad [B]
time = 0.02, size = 8, normalized size = 0.62 \begin {gather*} \frac {33\,x\,\left (x^{1/33}+34\right )}{34} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(x^(1/33) + 33,x)

[Out]

(33*x*(x^(1/33) + 34))/34

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