Optimal. Leaf size=26 \[ \text {Int}\left (\frac {1}{(c+d x) (a+i a \sinh (e+f x))},x\right ) \]
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Rubi [A]
time = 0.05, 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 = {}
\begin {gather*} \int \frac {1}{(c+d x) (a+i a \sinh (e+f x))} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {align*} \int \frac {1}{(c+d x) (a+i a \sinh (e+f x))} \, dx &=\int \frac {1}{(c+d x) (a+i a \sinh (e+f x))} \, dx\\ \end {align*}
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Mathematica [A]
time = 17.57, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {1}{(c+d x) (a+i a \sinh (e+f x))} \, dx \end {gather*}
Verification is not applicable to the result.
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Maple [A]
time = 180.00, size = 0, normalized size = 0.00 \[\int \frac {1}{\left (d x +c \right ) \left (a +i a \sinh \left (f x +e \right )\right )}\, dx\]
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 \begin {gather*} \text {Failed to integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}
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 \begin {gather*} \frac {2 i}{- i a c f - i a d f x + \left (a c f e^{e} + a d f x e^{e}\right ) e^{f x}} + \frac {2 i d \int \frac {1}{c^{2} e^{e} e^{f x} - i c^{2} + 2 c d x e^{e} e^{f x} - 2 i c d x + d^{2} x^{2} e^{e} e^{f x} - i d^{2} x^{2}}\, dx}{a f} \end {gather*}
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 \begin {gather*} \text {could not integrate} \end {gather*}
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 \begin {gather*} \int \frac {1}{\left (a+a\,\mathrm {sinh}\left (e+f\,x\right )\,1{}\mathrm {i}\right )\,\left (c+d\,x\right )} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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