\(\int F(c,d,\cosh (a+b x),r,s) \sinh (a+b x) \, dx\) [1015]

Optimal result

Integrand size = 18, antiderivative size = 18 \[ \int F(c,d,\cosh (a+b x),r,s) \sinh (a+b x) \, dx=\text {Int}(F(c,d,\cosh (a+b x),r,s) \sinh (a+b x),x) \]

[Out]

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

Rubi [N/A]

Not integrable

Time = 0.01 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.00, number of steps used = 0, number of rules used = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \[ \int F(c,d,\cosh (a+b x),r,s) \sinh (a+b x) \, dx=\int F(c,d,\cosh (a+b x),r,s) \sinh (a+b x) \, dx \]

[In]

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

[Out]

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

Rubi steps \begin{align*} \text {integral}& = \frac {\text {Subst}(\int F(c,d,x,r,s) \, dx,x,\cosh (a+b x))}{b} \\ \end{align*}

Mathematica [N/A]

Not integrable

Time = 0.05 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.11 \[ \int F(c,d,\cosh (a+b x),r,s) \sinh (a+b x) \, dx=\int F(c,d,\cosh (a+b x),r,s) \sinh (a+b x) \, dx \]

[In]

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

[Out]

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

Maple [N/A] (verified)

Not integrable

Time = 0.02 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.00

\[\int F \left (c , d , \cosh \left (b x +a \right ), r , s\right ) \sinh \left (b x +a \right )d x\]

[In]

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

[Out]

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

Fricas [N/A]

Not integrable

Time = 0.25 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.11 \[ \int F(c,d,\cosh (a+b x),r,s) \sinh (a+b x) \, dx=\int { F\left (c, d, \cosh \left (b x + a\right ), r, s\right ) \sinh \left (b x + a\right ) \,d x } \]

[In]

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

[Out]

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

Sympy [N/A]

Not integrable

Time = 0.54 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.83 \[ \int F(c,d,\cosh (a+b x),r,s) \sinh (a+b x) \, dx=\int F{\left (c,d,\cosh {\left (a + b x \right )},r,s \right )} \sinh {\left (a + b x \right )}\, dx \]

[In]

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

[Out]

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

Maxima [N/A]

Not integrable

Time = 0.30 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.11 \[ \int F(c,d,\cosh (a+b x),r,s) \sinh (a+b x) \, dx=\int { F\left (c, d, \cosh \left (b x + a\right ), r, s\right ) \sinh \left (b x + a\right ) \,d x } \]

[In]

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

[Out]

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

Giac [N/A]

Not integrable

Time = 0.26 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.11 \[ \int F(c,d,\cosh (a+b x),r,s) \sinh (a+b x) \, dx=\int { F\left (c, d, \cosh \left (b x + a\right ), r, s\right ) \sinh \left (b x + a\right ) \,d x } \]

[In]

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

[Out]

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

Mupad [N/A]

Not integrable

Time = 2.34 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.11 \[ \int F(c,d,\cosh (a+b x),r,s) \sinh (a+b x) \, dx=\int \mathrm {sinh}\left (a+b\,x\right )\,F\left (c,d,\mathrm {cosh}\left (a+b\,x\right ),r,s\right ) \,d x \]

[In]

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

[Out]

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