3.89 \(\int \text{Chi}(a+b x) \, dx\)

Optimal. Leaf size=27 \[ \frac{(a+b x) \text{Chi}(a+b x)}{b}-\frac{\sinh (a+b x)}{b} \]

[Out]

((a + b*x)*CoshIntegral[a + b*x])/b - Sinh[a + b*x]/b

________________________________________________________________________________________

Rubi [A]  time = 0.005794, antiderivative size = 27, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 6, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.167, Rules used = {6529} \[ \frac{(a+b x) \text{Chi}(a+b x)}{b}-\frac{\sinh (a+b x)}{b} \]

Antiderivative was successfully verified.

[In]

Int[CoshIntegral[a + b*x],x]

[Out]

((a + b*x)*CoshIntegral[a + b*x])/b - Sinh[a + b*x]/b

Rule 6529

Int[CoshIntegral[(a_.) + (b_.)*(x_)], x_Symbol] :> Simp[((a + b*x)*CoshIntegral[a + b*x])/b, x] - Simp[Sinh[a
+ b*x]/b, x] /; FreeQ[{a, b}, x]

Rubi steps

\begin{align*} \int \text{Chi}(a+b x) \, dx &=\frac{(a+b x) \text{Chi}(a+b x)}{b}-\frac{\sinh (a+b x)}{b}\\ \end{align*}

Mathematica [A]  time = 0.0351356, size = 42, normalized size = 1.56 \[ x \text{Chi}(a+b x)+\frac{a \text{Chi}(a+b x)}{b}-\frac{\sinh (a) \cosh (b x)}{b}-\frac{\cosh (a) \sinh (b x)}{b} \]

Antiderivative was successfully verified.

[In]

Integrate[CoshIntegral[a + b*x],x]

[Out]

(a*CoshIntegral[a + b*x])/b + x*CoshIntegral[a + b*x] - (Cosh[b*x]*Sinh[a])/b - (Cosh[a]*Sinh[b*x])/b

________________________________________________________________________________________

Maple [A]  time = 0.045, size = 26, normalized size = 1. \begin{align*}{\frac{ \left ( bx+a \right ){\it Chi} \left ( bx+a \right ) -\sinh \left ( bx+a \right ) }{b}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(Chi(b*x+a),x)

[Out]

1/b*((b*x+a)*Chi(b*x+a)-sinh(b*x+a))

________________________________________________________________________________________

Maxima [F]  time = 0., size = 0, normalized size = 0. \begin{align*} \int{\rm Chi}\left (b x + a\right )\,{d x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(Chi(b*x+a),x, algorithm="maxima")

[Out]

integrate(Chi(b*x + a), x)

________________________________________________________________________________________

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(Chi(b*x+a),x, algorithm="fricas")

[Out]

integral(cosh_integral(b*x + a), x)

________________________________________________________________________________________

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(Chi(b*x+a),x)

[Out]

Integral(Chi(a + b*x), x)

________________________________________________________________________________________

Giac [F]  time = 0., size = 0, normalized size = 0. \begin{align*} \int{\rm Chi}\left (b x + a\right )\,{d x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(Chi(b*x+a),x, algorithm="giac")

[Out]

integrate(Chi(b*x + a), x)