3.1014 $$\int \cosh (a+b x) F(c,d,\sinh (a+b x),r,s) \, dx$$

Optimal. Leaf size=20 $\text{CannotIntegrate}(\cosh (a+b x) F(c,d,\sinh (a+b x),r,s),x)$

[Out]

CannotIntegrate[Cosh[a + b*x]*F[c, d, Sinh[a + b*x], r, s], x]

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Rubi [A]  time = 0.0156299, antiderivative size = 0, normalized size of antiderivative = 0., number of steps used = 0, number of rules used = 0, integrand size = 0, $$\frac{\text{number of rules}}{\text{integrand size}}$$ = 0., Rules used = {} $\int \cosh (a+b x) F(c,d,\sinh (a+b x),r,s) \, dx$

Veriﬁcation is Not applicable to the result.

[In]

Int[Cosh[a + b*x]*F[c, d, Sinh[a + b*x], r, s],x]

[Out]

Defer[Subst][Defer[Int][F[c, d, x, r, s], x], x, Sinh[a + b*x]]/b

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*}

Mathematica [A]  time = 0.0329499, size = 0, normalized size = 0. $\int \cosh (a+b x) F(c,d,\sinh (a+b x),r,s) \, dx$

Veriﬁcation is Not applicable to the result.

[In]

Integrate[Cosh[a + b*x]*F[c, d, Sinh[a + b*x], r, s],x]

[Out]

Integrate[Cosh[a + b*x]*F[c, d, Sinh[a + b*x], r, s], x]

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Maple [A]  time = 0.029, size = 0, normalized size = 0. \begin{align*} \int \cosh \left ( bx+a \right ) F \left ( c,d,\sinh \left ( bx+a \right ) ,r,s \right ) \, dx \end{align*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

int(cosh(b*x+a)*F(c,d,sinh(b*x+a),r,s),x)

[Out]

int(cosh(b*x+a)*F(c,d,sinh(b*x+a),r,s),x)

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Maxima [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int F\left (c, d, \sinh \left (b x + a\right ), r, s\right ) \cosh \left (b x + a\right )\,{d x} \end{align*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(cosh(b*x+a)*F(c,d,sinh(b*x+a),r,s),x, algorithm="maxima")

[Out]

integrate(F(c, d, sinh(b*x + a), r, s)*cosh(b*x + a), x)

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Fricas [A]  time = 0., size = 0, normalized size = 0. \begin{align*}{\rm integral}\left (F\left (c, d, \sinh \left (b x + a\right ), r, s\right ) \cosh \left (b x + a\right ), x\right ) \end{align*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(cosh(b*x+a)*F(c,d,sinh(b*x+a),r,s),x, algorithm="fricas")

[Out]

integral(F(c, d, sinh(b*x + a), r, s)*cosh(b*x + a), x)

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Sympy [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int F{\left (c,d,\sinh{\left (a + b x \right )},r,s \right )} \cosh{\left (a + b x \right )}\, dx \end{align*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(cosh(b*x+a)*F(c,d,sinh(b*x+a),r,s),x)

[Out]

Integral(F(c, d, sinh(a + b*x), r, s)*cosh(a + b*x), x)

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Giac [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int F\left (c, d, \sinh \left (b x + a\right ), r, s\right ) \cosh \left (b x + a\right )\,{d x} \end{align*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(cosh(b*x+a)*F(c,d,sinh(b*x+a),r,s),x, algorithm="giac")

[Out]

integrate(F(c, d, sinh(b*x + a), r, s)*cosh(b*x + a), x)