Optimal. Leaf size=25 \[ \frac {\sinh (a) \text {Chi}\left (b x^n\right )}{n}+\frac {\cosh (a) \text {Shi}\left (b x^n\right )}{n} \]
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Rubi [A] time = 0.04, antiderivative size = 25, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 3, integrand size = 12, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.250, Rules used = {5318, 5317, 5316} \[ \frac {\sinh (a) \text {Chi}\left (b x^n\right )}{n}+\frac {\cosh (a) \text {Shi}\left (b x^n\right )}{n} \]
Antiderivative was successfully verified.
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Rule 5316
Rule 5317
Rule 5318
Rubi steps
\begin {align*} \int \frac {\sinh \left (a+b x^n\right )}{x} \, dx &=\cosh (a) \int \frac {\sinh \left (b x^n\right )}{x} \, dx+\sinh (a) \int \frac {\cosh \left (b x^n\right )}{x} \, dx\\ &=\frac {\text {Chi}\left (b x^n\right ) \sinh (a)}{n}+\frac {\cosh (a) \text {Shi}\left (b x^n\right )}{n}\\ \end {align*}
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Mathematica [A] time = 0.03, size = 23, normalized size = 0.92 \[ \frac {\sinh (a) \text {Chi}\left (b x^n\right )+\cosh (a) \text {Shi}\left (b x^n\right )}{n} \]
Antiderivative was successfully verified.
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fricas [B] time = 0.58, size = 55, normalized size = 2.20 \[ \frac {{\left (\cosh \relax (a) + \sinh \relax (a)\right )} {\rm Ei}\left (b \cosh \left (n \log \relax (x)\right ) + b \sinh \left (n \log \relax (x)\right )\right ) - {\left (\cosh \relax (a) - \sinh \relax (a)\right )} {\rm Ei}\left (-b \cosh \left (n \log \relax (x)\right ) - b \sinh \left (n \log \relax (x)\right )\right )}{2 \, n} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {\sinh \left (b x^{n} + a\right )}{x}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.02, size = 33, normalized size = 1.32 \[ \frac {{\mathrm e}^{-a} \Ei \left (1, b \,x^{n}\right )}{2 n}-\frac {{\mathrm e}^{a} \Ei \left (1, -b \,x^{n}\right )}{2 n} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.61, size = 30, normalized size = 1.20 \[ -\frac {{\rm Ei}\left (-b x^{n}\right ) e^{\left (-a\right )}}{2 \, n} + \frac {{\rm Ei}\left (b x^{n}\right ) e^{a}}{2 \, n} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [F] time = 0.00, size = -1, normalized size = -0.04 \[ \int \frac {\mathrm {sinh}\left (a+b\,x^n\right )}{x} \,d x \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {\sinh {\left (a + b x^{n} \right )}}{x}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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