3.1016 \(\int F(c,d,\tanh (a+b x),r,s) \text {sech}^2(a+b x) \, dx\)

Optimal. Leaf size=23 \[ \text {Int}\left (\text {sech}^2(a+b x) F(c,d,\tanh (a+b x),r,s),x\right ) \]

[Out]

CannotIntegrate(F(c,d,tanh(b*x+a),r,s)*sech(b*x+a)^2,x)

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Rubi [A]  time = 0.02, 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 = {} \[ \int F(c,d,\tanh (a+b x),r,s) \text {sech}^2(a+b x) \, dx \]

Verification is Not applicable to the result.

[In]

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

[Out]

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

Rubi steps

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

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Mathematica [A]  time = 0.08, size = 0, normalized size = 0.00 \[ \int F(c,d,\tanh (a+b x),r,s) \text {sech}^2(a+b x) \, dx \]

Verification is Not applicable to the result.

[In]

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

[Out]

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

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fricas [A]  time = 0.41, size = 0, normalized size = 0.00 \[ {\rm integral}\left (F\left (c, d, \tanh \left (b x + a\right ), r, s\right ) \operatorname {sech}\left (b x + a\right )^{2}, x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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giac [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int F\left (c, d, \tanh \left (b x + a\right ), r, s\right ) \operatorname {sech}\left (b x + a\right )^{2}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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maple [A]  time = 0.16, size = 0, normalized size = 0.00 \[ \int F \left (c , d , \tanh \left (b x +a \right ), r , s\right ) \mathrm {sech}\left (b x +a \right )^{2}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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maxima [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int F\left (c, d, \tanh \left (b x + a\right ), r, s\right ) \operatorname {sech}\left (b x + a\right )^{2}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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mupad [A]  time = 0.00, size = -1, normalized size = -0.04 \[ \int \frac {F\left (c,d,\mathrm {tanh}\left (a+b\,x\right ),r,s\right )}{{\mathrm {cosh}\left (a+b\,x\right )}^2} \,d x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(F(c, d, tanh(a + b*x), r, s)/cosh(a + b*x)^2,x)

[Out]

int(F(c, d, tanh(a + b*x), r, s)/cosh(a + b*x)^2, x)

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sympy [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int F{\left (c,d,\tanh {\left (a + b x \right )},r,s \right )} \operatorname {sech}^{2}{\left (a + b x \right )}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(F(c,d,tanh(b*x+a),r,s)*sech(b*x+a)**2,x)

[Out]

Integral(F(c, d, tanh(a + b*x), r, s)*sech(a + b*x)**2, x)

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