Optimal. Leaf size=7 \[ \log (\sinh (x)+i) \]
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Rubi [A] time = 0.02, antiderivative size = 7, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.182, Rules used = {2667, 31} \[ \log (\sinh (x)+i) \]
Antiderivative was successfully verified.
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Rule 31
Rule 2667
Rubi steps
\begin {align*} \int \frac {\cosh (x)}{i+\sinh (x)} \, dx &=\operatorname {Subst}\left (\int \frac {1}{i+x} \, dx,x,\sinh (x)\right )\\ &=\log (i+\sinh (x))\\ \end {align*}
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Mathematica [A] time = 0.01, size = 7, normalized size = 1.00 \[ \log (\sinh (x)+i) \]
Antiderivative was successfully verified.
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fricas [B] time = 0.50, size = 11, normalized size = 1.57 \[ -x + 2 \, \log \left (e^{x} + i\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.30, size = 11, normalized size = 1.57 \[ -x + 2 \, \log \left (e^{x} + i\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.02, size = 7, normalized size = 1.00 \[ \ln \left (i+\sinh \relax (x )\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.32, size = 5, normalized size = 0.71 \[ \log \left (\sinh \relax (x) + i\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.47, size = 10, normalized size = 1.43 \[ \ln \left (\mathrm {cosh}\relax (x)\right )-\mathrm {atan}\left (\mathrm {sinh}\relax (x)\right )\,1{}\mathrm {i} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.13, size = 15, normalized size = 2.14 \[ x \left (1 + 2 i\right ) - 2 i \log {\left (e^{x} + i \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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