3.646 \(\int F(c,d,\tan (a+b x),r,s) \sec ^2(a+b x) \, dx\)

Optimal. Leaf size=22 \[ \text{CannotIntegrate}\left (\sec ^2(a+b x) F(c,d,\tan (a+b x),r,s),x\right ) \]

[Out]

CannotIntegrate[F[c, d, Tan[a + b*x], r, s]*Sec[a + b*x]^2, x]

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Rubi [A]  time = 0.0161296, 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 = {} \[ \int F(c,d,\tan (a+b x),r,s) \sec ^2(a+b x) \, dx \]

Verification is Not applicable to the result.

[In]

Int[F[c, d, Tan[a + b*x], r, s]*Sec[a + b*x]^2,x]

[Out]

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

Rubi steps

\begin{align*} \int F(c,d,\tan (a+b x),r,s) \sec ^2(a+b x) \, dx &=\frac{\operatorname{Subst}(\int F(c,d,x,r,s) \, dx,x,\tan (a+b x))}{b}\\ \end{align*}

Mathematica [A]  time = 0.0776369, size = 0, normalized size = 0. \[ \int F(c,d,\tan (a+b x),r,s) \sec ^2(a+b x) \, dx \]

Verification is Not applicable to the result.

[In]

Integrate[F[c, d, Tan[a + b*x], r, s]*Sec[a + b*x]^2,x]

[Out]

Integrate[F[c, d, Tan[a + b*x], r, s]*Sec[a + b*x]^2, x]

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Maple [A]  time = 0.026, size = 0, normalized size = 0. \begin{align*} \int F \left ( c,d,\tan \left ( bx+a \right ) ,r,s \right ) \left ( \sec \left ( bx+a \right ) \right ) ^{2}\, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(F(c,d,tan(b*x+a),r,s)*sec(b*x+a)^2,x)

[Out]

int(F(c,d,tan(b*x+a),r,s)*sec(b*x+a)^2,x)

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Maxima [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int F\left (c, d, \tan \left (b x + a\right ), r, s\right ) \sec \left (b x + a\right )^{2}\,{d x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(F(c,d,tan(b*x+a),r,s)*sec(b*x+a)^2,x, algorithm="maxima")

[Out]

integrate(F(c, d, tan(b*x + a), r, s)*sec(b*x + a)^2, x)

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Fricas [A]  time = 0., size = 0, normalized size = 0. \begin{align*}{\rm integral}\left (F\left (c, d, \tan \left (b x + a\right ), r, s\right ) \sec \left (b x + a\right )^{2}, x\right ) \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(F(c,d,tan(b*x+a),r,s)*sec(b*x+a)^2,x, algorithm="fricas")

[Out]

integral(F(c, d, tan(b*x + a), r, s)*sec(b*x + a)^2, x)

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Sympy [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int F{\left (c,d,\tan{\left (a + b x \right )},r,s \right )} \sec ^{2}{\left (a + b x \right )}\, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(F(c,d,tan(b*x+a),r,s)*sec(b*x+a)**2,x)

[Out]

Integral(F(c, d, tan(a + b*x), r, s)*sec(a + b*x)**2, x)

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Giac [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int F\left (c, d, \tan \left (b x + a\right ), r, s\right ) \sec \left (b x + a\right )^{2}\,{d x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(F(c,d,tan(b*x+a),r,s)*sec(b*x+a)^2,x, algorithm="giac")

[Out]

integrate(F(c, d, tan(b*x + a), r, s)*sec(b*x + a)^2, x)