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 = 0.02, 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 = {} \[ \int \cosh (a+b x) F(c,d,\sinh (a+b x),r,s) \, dx \]
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 {\operatorname {Subst}(\int F(c,d,x,r,s) \, dx,x,\sinh (a+b x))}{b}\\ \end {align*}
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Mathematica [A] time = 0.04, size = 0, normalized size = 0.00 \[ \int \cosh (a+b x) F(c,d,\sinh (a+b x),r,s) \, dx \]
Verification is Not applicable to the result.
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fricas [A] time = 0.41, size = 0, normalized size = 0.00 \[ {\rm integral}\left (F\left (c, d, \sinh \left (b x + a\right ), r, s\right ) \cosh \left (b x + a\right ), x\right ) \]
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 \[ \int F\left (c, d, \sinh \left (b x + a\right ), r, s\right ) \cosh \left (b x + a\right )\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.11, 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 \[ \int F\left (c, d, \sinh \left (b x + a\right ), r, s\right ) \cosh \left (b x + a\right )\,{d x} \]
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 \[ \int \mathrm {cosh}\left (a+b\,x\right )\,F\left (c,d,\mathrm {sinh}\left (a+b\,x\right ),r,s\right ) \,d x \]
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 \[ \int F{\left (c,d,\sinh {\left (a + b x \right )},r,s \right )} \cosh {\left (a + b x \right )}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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