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