3.1911 \(\int (33+\sqrt [33]{x}) \, dx\)

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

[Out]

33*x + (33*x^(34/33))/34

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Rubi [A]  time = 0.0016099, antiderivative size = 13, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 0, integrand size = 7, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0., Rules used = {} \[ \frac{33 x^{34/33}}{34}+33 x \]

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*}

Mathematica [A]  time = 0.0013808, size = 13, normalized size = 1. \[ \frac{33 x^{34/33}}{34}+33 x \]

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 = 0.001, size = 10, normalized size = 0.8 \begin{align*} 33\,x+{\frac{33}{34}{x}^{{\frac{34}{33}}}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(33+x^(1/33),x)

[Out]

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

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Maxima [A]  time = 0.95642, size = 12, normalized size = 0.92 \begin{align*} \frac{33}{34} \, x^{\frac{34}{33}} + 33 \, x \end{align*}

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 = 1.91538, size = 32, normalized size = 2.46 \begin{align*} \frac{33}{34} \, x^{\frac{34}{33}} + 33 \, x \end{align*}

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 = 0.052312, size = 10, normalized size = 0.77 \begin{align*} \frac{33 x^{\frac{34}{33}}}{34} + 33 x \end{align*}

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 = 1.07811, size = 12, normalized size = 0.92 \begin{align*} \frac{33}{34} \, x^{\frac{34}{33}} + 33 \, x \end{align*}

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