3.68 \(\int \sqrt{c+d x} \text{sech}(a+b x) \, dx\)

Optimal. Leaf size=18 \[ \text{Unintegrable}\left (\sqrt{c+d x} \text{sech}(a+b x),x\right ) \]

[Out]

Unintegrable[Sqrt[c + d*x]*Sech[a + b*x], x]

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Rubi [A]  time = 0.0283211, 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 = {} \[ \int \sqrt{c+d x} \text{sech}(a+b x) \, dx \]

Verification is Not applicable to the result.

[In]

Int[Sqrt[c + d*x]*Sech[a + b*x],x]

[Out]

Defer[Int][Sqrt[c + d*x]*Sech[a + b*x], x]

Rubi steps

\begin{align*} \int \sqrt{c+d x} \text{sech}(a+b x) \, dx &=\int \sqrt{c+d x} \text{sech}(a+b x) \, dx\\ \end{align*}

Mathematica [A]  time = 11.1617, size = 0, normalized size = 0. \[ \int \sqrt{c+d x} \text{sech}(a+b x) \, dx \]

Verification is Not applicable to the result.

[In]

Integrate[Sqrt[c + d*x]*Sech[a + b*x],x]

[Out]

Integrate[Sqrt[c + d*x]*Sech[a + b*x], x]

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Maple [A]  time = 0.068, size = 0, normalized size = 0. \begin{align*} \int{\rm sech} \left (bx+a\right )\sqrt{dx+c}\, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(sech(b*x+a)*(d*x+c)^(1/2),x)

[Out]

int(sech(b*x+a)*(d*x+c)^(1/2),x)

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Maxima [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \sqrt{d x + c} \operatorname{sech}\left (b x + a\right )\,{d x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(sech(b*x+a)*(d*x+c)^(1/2),x, algorithm="maxima")

[Out]

integrate(sqrt(d*x + c)*sech(b*x + a), x)

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Fricas [A]  time = 0., size = 0, normalized size = 0. \begin{align*}{\rm integral}\left (\sqrt{d x + c} \operatorname{sech}\left (b x + a\right ), x\right ) \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(sech(b*x+a)*(d*x+c)^(1/2),x, algorithm="fricas")

[Out]

integral(sqrt(d*x + c)*sech(b*x + a), x)

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Sympy [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \sqrt{c + d x} \operatorname{sech}{\left (a + b x \right )}\, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(sech(b*x+a)*(d*x+c)**(1/2),x)

[Out]

Integral(sqrt(c + d*x)*sech(a + b*x), x)

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Giac [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \sqrt{d x + c} \operatorname{sech}\left (b x + a\right )\,{d x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(sech(b*x+a)*(d*x+c)^(1/2),x, algorithm="giac")

[Out]

integrate(sqrt(d*x + c)*sech(b*x + a), x)