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

Optimal. Leaf size=24 \[ \text {Int}\left (\frac {\sqrt [3]{a+i a \sinh (e+f x)}}{x},x\right ) \]

[Out]

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

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Rubi [A]  time = 0.07, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, 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*}

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Mathematica [A]  time = 3.96, size = 0, normalized size = 0.00 \[ \int \frac {\sqrt [3]{a+i a \sinh (e+f x)}}{x} \, dx \]

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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fricas [F(-2)]  time = 0.00, size = 0, normalized size = 0.00 \[ \text {Exception raised: TypeError} \]

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: TypeError >>  Error detected within library code:   integrate: implementation incomplete (ha
s polynomial part)

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giac [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {{\left (i \, a \sinh \left (f x + e\right ) + a\right )}^{\frac {1}{3}}}{x}\,{d x} \]

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)

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maple [A]  time = 0.11, size = 0, normalized size = 0.00 \[ \int \frac {\left (a +i a \sinh \left (f x +e \right )\right )^{\frac {1}{3}}}{x}\, dx \]

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 = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {{\left (i \, a \sinh \left (f x + e\right ) + a\right )}^{\frac {1}{3}}}{x}\,{d x} \]

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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mupad [A]  time = 0.00, size = -1, normalized size = -0.04 \[ \int \frac {{\left (a+a\,\mathrm {sinh}\left (e+f\,x\right )\,1{}\mathrm {i}\right )}^{1/3}}{x} \,d x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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sympy [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {\sqrt [3]{i a \left (\sinh {\left (e + f x \right )} - i\right )}}{x}\, dx \]

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

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