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

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

[Out]

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

Verification is Not applicable to the result.

[In]

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

[Out]

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

Rubi steps

\begin {align*} \int \cos (a+b x) F(c,d,\sin (a+b x),r,s) \, dx &=\frac {\operatorname {Subst}(\int F(c,d,x,r,s) \, dx,x,\sin (a+b x))}{b}\\ \end {align*}

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Mathematica [A]  time = 0.03, size = 0, normalized size = 0.00 \[ \int \cos (a+b x) F(c,d,\sin (a+b x),r,s) \, dx \]

Verification is Not applicable to the result.

[In]

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

[Out]

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

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fricas [A]  time = 0.90, size = 0, normalized size = 0.00 \[ {\rm integral}\left (F\left (c, d, \sin \left (b x + a\right ), r, s\right ) \cos \left (b x + a\right ), x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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giac [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int F\left (c, d, \sin \left (b x + a\right ), r, s\right ) \cos \left (b x + a\right )\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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maple [A]  time = 0.03, size = 0, normalized size = 0.00 \[ \int \cos \left (b x +a \right ) F \left (c , d , \sin \left (b x +a \right ), r , s\right )\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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maxima [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int F\left (c, d, \sin \left (b x + a\right ), r, s\right ) \cos \left (b x + a\right )\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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mupad [A]  time = 0.00, size = -1, normalized size = -0.05 \[ \int \cos \left (a+b\,x\right )\,F\left (c,d,\sin \left (a+b\,x\right ),r,s\right ) \,d x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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sympy [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int F{\left (c,d,\sin {\left (a + b x \right )},r,s \right )} \cos {\left (a + b x \right )}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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