Optimal. Leaf size=27 \[ \frac {(a+b x) \text {Shi}(a+b x)}{b}-\frac {\cosh (a+b x)}{b} \]
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Rubi [A] time = 0.01, antiderivative size = 27, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 6, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.167, Rules used = {6528} \[ \frac {(a+b x) \text {Shi}(a+b x)}{b}-\frac {\cosh (a+b x)}{b} \]
Antiderivative was successfully verified.
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Rule 6528
Rubi steps
\begin {align*} \int \text {Shi}(a+b x) \, dx &=-\frac {\cosh (a+b x)}{b}+\frac {(a+b x) \text {Shi}(a+b x)}{b}\\ \end {align*}
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Mathematica [A] time = 0.04, size = 42, normalized size = 1.56 \[ x \text {Shi}(a+b x)+\frac {a \text {Shi}(a+b x)}{b}-\frac {\sinh (a) \sinh (b x)}{b}-\frac {\cosh (a) \cosh (b x)}{b} \]
Antiderivative was successfully verified.
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fricas [F] time = 2.22, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\operatorname {Shi}\left (b x + a\right ), x\right ) \]
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 \[ \int {\rm Shi}\left (b x + a\right )\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 26, normalized size = 0.96 \[ \frac {\left (b x +a \right ) \Shi \left (b x +a \right )-\cosh \left (b x +a \right )}{b} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int {\rm Shi}\left (b x + a\right )\,{d x} \]
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 \[ x\,\mathrm {sinhint}\left (a+b\,x\right )-\frac {{\mathrm {e}}^{a+b\,x}}{2\,b}-\frac {{\mathrm {e}}^{-a-b\,x}}{2\,b}+\frac {a\,\mathrm {sinhint}\left (a+b\,x\right )}{b} \]
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 \[ \int \operatorname {Shi}{\left (a + b x \right )}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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