3.150 \(\int \frac{\sqrt [3]{a+i a \sinh (e+f x)}}{x} \, dx\)

Optimal. Leaf size=23 \[ \text{Unintegrable}\left (\frac{\sqrt [3]{a+i a \sinh (e+f x)}}{x},x\right ) \]

[Out]

Unintegrable[(a + I*a*Sinh[e + f*x])^(1/3)/x, x]

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Rubi [A]  time = 0.0733574, antiderivative size = 0, normalized size of antiderivative = 0., number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0., Rules used = {} \[ \int \frac{\sqrt [3]{a+i a \sinh (e+f x)}}{x} \, dx \]

Verification is Not applicable to the result.

[In]

Int[(a + I*a*Sinh[e + f*x])^(1/3)/x,x]

[Out]

Defer[Int][(a + I*a*Sinh[e + f*x])^(1/3)/x, x]

Rubi steps

\begin{align*} \int \frac{\sqrt [3]{a+i a \sinh (e+f x)}}{x} \, dx &=\int \frac{\sqrt [3]{a+i a \sinh (e+f x)}}{x} \, dx\\ \end{align*}

Mathematica [A]  time = 3.97186, size = 0, normalized size = 0. \[ \int \frac{\sqrt [3]{a+i a \sinh (e+f x)}}{x} \, dx \]

Verification is Not applicable to the result.

[In]

Integrate[(a + I*a*Sinh[e + f*x])^(1/3)/x,x]

[Out]

Integrate[(a + I*a*Sinh[e + f*x])^(1/3)/x, x]

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Maple [A]  time = 0.073, size = 0, normalized size = 0. \begin{align*} \int{\frac{1}{x}\sqrt [3]{a+ia\sinh \left ( fx+e \right ) }}\, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((a+I*a*sinh(f*x+e))^(1/3)/x,x)

[Out]

int((a+I*a*sinh(f*x+e))^(1/3)/x,x)

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Maxima [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{{\left (i \, a \sinh \left (f x + e\right ) + a\right )}^{\frac{1}{3}}}{x}\,{d x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((a+I*a*sinh(f*x+e))^(1/3)/x,x, algorithm="maxima")

[Out]

integrate((I*a*sinh(f*x + e) + a)^(1/3)/x, x)

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Fricas [F(-2)]  time = 0., size = 0, normalized size = 0. \begin{align*} \text{Exception raised: UnboundLocalError} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((a+I*a*sinh(f*x+e))^(1/3)/x,x, algorithm="fricas")

[Out]

Exception raised: UnboundLocalError

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Sympy [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{\sqrt [3]{a \left (i \sinh{\left (e + f x \right )} + 1\right )}}{x}\, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((a+I*a*sinh(f*x+e))**(1/3)/x,x)

[Out]

Integral((a*(I*sinh(e + f*x) + 1))**(1/3)/x, x)

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Giac [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{{\left (i \, a \sinh \left (f x + e\right ) + a\right )}^{\frac{1}{3}}}{x}\,{d x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((a+I*a*sinh(f*x+e))^(1/3)/x,x, algorithm="giac")

[Out]

integrate((I*a*sinh(f*x + e) + a)^(1/3)/x, x)