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

Optimal result

Integrand size = 7, antiderivative size = 13 \[ \int \left (33+\sqrt [33]{x}\right ) \, dx=33 x+\frac {33 x^{34/33}}{34} \]

[Out]

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

Rubi [A] (verified)

Time = 0.00 (sec) , antiderivative size = 13, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \[ \int \left (33+\sqrt [33]{x}\right ) \, dx=\frac {33 x^{34/33}}{34}+33 x \]

[In]

Int[33 + x^(1/33),x]

[Out]

33*x + (33*x^(34/33))/34

Rubi steps \begin{align*} \text {integral}& = 33 x+\frac {33 x^{34/33}}{34} \\ \end{align*}

Mathematica [A] (verified)

Time = 0.00 (sec) , antiderivative size = 13, normalized size of antiderivative = 1.00 \[ \int \left (33+\sqrt [33]{x}\right ) \, dx=33 x+\frac {33 x^{34/33}}{34} \]

[In]

Integrate[33 + x^(1/33),x]

[Out]

33*x + (33*x^(34/33))/34

Maple [A] (verified)

Time = 0.24 (sec) , antiderivative size = 10, normalized size of antiderivative = 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	\(33 x +\frac {33 x^{\frac {34}{33}}}{34}\)	\(10\)
parts	\(33 x +\frac {33 x^{\frac {34}{33}}}{34}\)	\(10\)
trager	\(-33+33 x +\frac {33 x^{\frac {34}{33}}}{34}\)	\(11\)

[In]

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

[Out]

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

Fricas [A] (verification not implemented)

none

Time = 0.22 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.69 \[ \int \left (33+\sqrt [33]{x}\right ) \, dx=\frac {33}{34} \, x^{\frac {34}{33}} + 33 \, x \]

[In]

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

[Out]

33/34*x^(34/33) + 33*x

Sympy [A] (verification not implemented)

Time = 0.02 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.77 \[ \int \left (33+\sqrt [33]{x}\right ) \, dx=\frac {33 x^{\frac {34}{33}}}{34} + 33 x \]

[In]

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

[Out]

33*x**(34/33)/34 + 33*x

Maxima [A] (verification not implemented)

none

Time = 0.20 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.69 \[ \int \left (33+\sqrt [33]{x}\right ) \, dx=\frac {33}{34} \, x^{\frac {34}{33}} + 33 \, x \]

[In]

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

[Out]

33/34*x^(34/33) + 33*x

Giac [A] (verification not implemented)

none

Time = 0.27 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.69 \[ \int \left (33+\sqrt [33]{x}\right ) \, dx=\frac {33}{34} \, x^{\frac {34}{33}} + 33 \, x \]

[In]

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

[Out]

33/34*x^(34/33) + 33*x

Mupad [B] (verification not implemented)

Time = 0.03 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.62 \[ \int \left (33+\sqrt [33]{x}\right ) \, dx=\frac {33\,x\,\left (x^{1/33}+34\right )}{34} \]

[In]

int(x^(1/33) + 33,x)

[Out]

(33*x*(x^(1/33) + 34))/34