3.11.14 \(\int \cosh (a+b x) F(c,d,\sinh (a+b x),r,s) \, dx\) [1014]

Optimal. Leaf size=21 \[ \text {Int}(\cosh (a+b x) F(c,d,\sinh (a+b x),r,s),x) \]

[Out]

CannotIntegrate(cosh(b*x+a)*F(c,d,sinh(b*x+a),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.

[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 {\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.

[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 = 0.43, 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.

[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 = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Failed to integrate} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[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 = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[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 = 0.00, 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.

[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 = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[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)

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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.

[In]

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

[Out]

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

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