3.48 \(\int \frac{\cosh (b x) \text{Shi}(b x)}{x} \, dx\)

Optimal. Leaf size=14 \[ \text{CannotIntegrate}\left (\frac{\text{Shi}(b x) \cosh (b x)}{x},x\right ) \]

[Out]

CannotIntegrate[(Cosh[b*x]*SinhIntegral[b*x])/x, x]

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Rubi [A]  time = 0.0279681, 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 = {} \[ \int \frac{\cosh (b x) \text{Shi}(b x)}{x} \, dx \]

Verification is Not applicable to the result.

[In]

Int[(Cosh[b*x]*SinhIntegral[b*x])/x,x]

[Out]

Defer[Int][(Cosh[b*x]*SinhIntegral[b*x])/x, x]

Rubi steps

\begin{align*} \int \frac{\cosh (b x) \text{Shi}(b x)}{x} \, dx &=\int \frac{\cosh (b x) \text{Shi}(b x)}{x} \, dx\\ \end{align*}

Mathematica [A]  time = 0.26094, size = 0, normalized size = 0. \[ \int \frac{\cosh (b x) \text{Shi}(b x)}{x} \, dx \]

Verification is Not applicable to the result.

[In]

Integrate[(Cosh[b*x]*SinhIntegral[b*x])/x,x]

[Out]

Integrate[(Cosh[b*x]*SinhIntegral[b*x])/x, x]

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Maple [A]  time = 0.056, size = 0, normalized size = 0. \begin{align*} \int{\frac{\cosh \left ( bx \right ){\it Shi} \left ( bx \right ) }{x}}\, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(cosh(b*x)*Shi(b*x)/x,x)

[Out]

int(cosh(b*x)*Shi(b*x)/x,x)

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Maxima [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{{\rm Shi}\left (b x\right ) \cosh \left (b x\right )}{x}\,{d x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(cosh(b*x)*Shi(b*x)/x,x, algorithm="maxima")

[Out]

integrate(Shi(b*x)*cosh(b*x)/x, x)

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Fricas [A]  time = 0., size = 0, normalized size = 0. \begin{align*}{\rm integral}\left (\frac{\cosh \left (b x\right ) \operatorname{Shi}\left (b x\right )}{x}, x\right ) \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(cosh(b*x)*Shi(b*x)/x,x, algorithm="fricas")

[Out]

integral(cosh(b*x)*sinh_integral(b*x)/x, x)

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Sympy [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{\cosh{\left (b x \right )} \operatorname{Shi}{\left (b x \right )}}{x}\, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(cosh(b*x)*Shi(b*x)/x,x)

[Out]

Integral(cosh(b*x)*Shi(b*x)/x, x)

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Giac [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{{\rm Shi}\left (b x\right ) \cosh \left (b x\right )}{x}\,{d x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(cosh(b*x)*Shi(b*x)/x,x, algorithm="giac")

[Out]

integrate(Shi(b*x)*cosh(b*x)/x, x)