\(\int F(c,d,\cos (a+b x),r,s) \sin (a+b x) \, dx\) [644]

Optimal result

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

[Out]

CannotIntegrate(F(c,d,cos(b*x+a),r,s)*sin(b*x+a),x)

Rubi [N/A]

Not integrable

Time = 0.02 (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 = {} \[ \int F(c,d,\cos (a+b x),r,s) \sin (a+b x) \, dx=\int F(c,d,\cos (a+b x),r,s) \sin (a+b x) \, dx \]

[In]

Int[F[c, d, Cos[a + b*x], r, s]*Sin[a + b*x],x]

[Out]

-(Defer[Subst][Defer[Int][F[c, d, x, r, s], x], x, Cos[a + b*x]]/b)

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

Mathematica [N/A]

Not integrable

Time = 0.08 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.11 \[ \int F(c,d,\cos (a+b x),r,s) \sin (a+b x) \, dx=\int F(c,d,\cos (a+b x),r,s) \sin (a+b x) \, dx \]

[In]

Integrate[F[c, d, Cos[a + b*x], r, s]*Sin[a + b*x],x]

[Out]

Integrate[F[c, d, Cos[a + b*x], r, s]*Sin[a + b*x], x]

Maple [N/A] (verified)

Not integrable

Time = 0.12 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.00

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

[In]

int(F(c,d,cos(b*x+a),r,s)*sin(b*x+a),x)

[Out]

int(F(c,d,cos(b*x+a),r,s)*sin(b*x+a),x)

Fricas [N/A]

Not integrable

Time = 0.23 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.11 \[ \int F(c,d,\cos (a+b x),r,s) \sin (a+b x) \, dx=\int { F\left (c, d, \cos \left (b x + a\right ), r, s\right ) \sin \left (b x + a\right ) \,d x } \]

[In]

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

[Out]

integral(F(c, d, cos(b*x + a), r, s)*sin(b*x + a), x)

Sympy [N/A]

Not integrable

Time = 0.44 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.83 \[ \int F(c,d,\cos (a+b x),r,s) \sin (a+b x) \, dx=\int F{\left (c,d,\cos {\left (a + b x \right )},r,s \right )} \sin {\left (a + b x \right )}\, dx \]

[In]

integrate(F(c,d,cos(b*x+a),r,s)*sin(b*x+a),x)

[Out]

Integral(F(c, d, cos(a + b*x), r, s)*sin(a + b*x), x)

Maxima [N/A]

Not integrable

Time = 0.31 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.11 \[ \int F(c,d,\cos (a+b x),r,s) \sin (a+b x) \, dx=\int { F\left (c, d, \cos \left (b x + a\right ), r, s\right ) \sin \left (b x + a\right ) \,d x } \]

[In]

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

[Out]

integrate(F(c, d, cos(b*x + a), r, s)*sin(b*x + a), x)

Giac [N/A]

Not integrable

Time = 0.28 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.11 \[ \int F(c,d,\cos (a+b x),r,s) \sin (a+b x) \, dx=\int { F\left (c, d, \cos \left (b x + a\right ), r, s\right ) \sin \left (b x + a\right ) \,d x } \]

[In]

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

[Out]

integrate(F(c, d, cos(b*x + a), r, s)*sin(b*x + a), x)

Mupad [N/A]

Not integrable

Time = 26.71 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.11 \[ \int F(c,d,\cos (a+b x),r,s) \sin (a+b x) \, dx=\int \sin \left (a+b\,x\right )\,F\left (c,d,\cos \left (a+b\,x\right ),r,s\right ) \,d x \]

[In]

int(sin(a + b*x)*F(c, d, cos(a + b*x), r, s),x)

[Out]

int(sin(a + b*x)*F(c, d, cos(a + b*x), r, s), x)