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

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

________________________________________________________________________________________

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*}

________________________________________________________________________________________

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

Antiderivative was successfully verified.

[In]

Integrate[33 + x^(1/33),x]

[Out]

33*x + (33*x^(34/33))/34

________________________________________________________________________________________

IntegrateAlgebraic [A]  time = 0.01, size = 13, normalized size = 1.00 \begin {gather*} \frac {33 x^{34/33}}{34}+33 x \end {gather*}

Antiderivative was successfully verified.

[In]

IntegrateAlgebraic[33 + x^(1/33),x]

[Out]

33*x + (33*x^(34/33))/34

________________________________________________________________________________________

fricas [A]  time = 1.20, 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

________________________________________________________________________________________

giac [A]  time = 0.85, 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

________________________________________________________________________________________

maple [A]  time = 0.00, 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]

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

[Out]

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

________________________________________________________________________________________

maxima [A]  time = 1.00, 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

________________________________________________________________________________________

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

________________________________________________________________________________________

sympy [A]  time = 0.06, 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

________________________________________________________________________________________