Optimal. Leaf size=21 \[ \text {Int}(\cosh (a+b x) F(c,d,\sinh (a+b x),r,s),x) \]
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Rubi [A]
time = 0.01, 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 \cosh (a+b x) F(c,d,\sinh (a+b x),r,s) \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {align*} \int \cosh (a+b x) F(c,d,\sinh (a+b x),r,s) \, dx &=\frac {\text {Subst}(\int F(c,d,x,r,s) \, dx,x,\sinh (a+b x))}{b}\\ \end {align*}
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Mathematica [A]
time = 0.03, size = 0, normalized size = 0.00 \begin {gather*} \int \cosh (a+b x) F(c,d,\sinh (a+b x),r,s) \, dx \end {gather*}
Verification is not applicable to the result.
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Maple [A]
time = 0.43, size = 0, normalized size = 0.00 \[\int \cosh \left (b x +a \right ) F \left (c , d , \sinh \left (b x +a \right ), r , s\right )\, dx\]
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*} \int F{\left (c,d,\sinh {\left (a + b x \right )},r,s \right )} \cosh {\left (a + b x \right )}\, dx \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 = -0.05 \begin {gather*} \int \mathrm {cosh}\left (a+b\,x\right )\,F\left (c,d,\mathrm {sinh}\left (a+b\,x\right ),r,s\right ) \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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