\(\int x^m \text {Shi}(a+b x) \, dx\) [17]

Optimal result

Integrand size = 10, antiderivative size = 10 \[ \int x^m \text {Shi}(a+b x) \, dx=\frac {x^{1+m} \text {Shi}(a+b x)}{1+m}-\frac {b \text {Int}\left (\frac {x^{1+m} \sinh (a+b x)}{a+b x},x\right )}{1+m} \]

[Out]

-b*CannotIntegrate(x^(1+m)*sinh(b*x+a)/(b*x+a),x)/(1+m)+x^(1+m)*Shi(b*x+a)/(1+m)

Rubi [N/A]

Not integrable

Time = 0.22 (sec) , antiderivative size = 10, normalized size of antiderivative = 1.00, number of steps used = 0, number of rules used = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \[ \int x^m \text {Shi}(a+b x) \, dx=\int x^m \text {Shi}(a+b x) \, dx \]

[In]

Int[x^m*SinhIntegral[a + b*x],x]

[Out]

(x^(1 + m)*SinhIntegral[a + b*x])/(1 + m) - (b*Defer[Int][(x^(1 + m)*Sinh[a + b*x])/(a + b*x), x])/(1 + m)

Rubi steps \begin{align*} \text {integral}& = \frac {x^{1+m} \text {Shi}(a+b x)}{1+m}-\frac {b \int \frac {x^{1+m} \sinh (a+b x)}{a+b x} \, dx}{1+m} \\ \end{align*}

Mathematica [N/A]

Not integrable

Time = 6.19 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.20 \[ \int x^m \text {Shi}(a+b x) \, dx=\int x^m \text {Shi}(a+b x) \, dx \]

[In]

Integrate[x^m*SinhIntegral[a + b*x],x]

[Out]

Integrate[x^m*SinhIntegral[a + b*x], x]

Maple [N/A] (verified)

Not integrable

Time = 0.28 (sec) , antiderivative size = 10, normalized size of antiderivative = 1.00

\[\int x^{m} \operatorname {Shi}\left (b x +a \right )d x\]

[In]

int(x^m*Shi(b*x+a),x)

[Out]

int(x^m*Shi(b*x+a),x)

Fricas [N/A]

Not integrable

Time = 0.25 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.20 \[ \int x^m \text {Shi}(a+b x) \, dx=\int { x^{m} {\rm Shi}\left (b x + a\right ) \,d x } \]

[In]

integrate(x^m*Shi(b*x+a),x, algorithm="fricas")

[Out]

integral(x^m*sinh_integral(b*x + a), x)

Sympy [N/A]

Not integrable

Time = 0.62 (sec) , antiderivative size = 10, normalized size of antiderivative = 1.00 \[ \int x^m \text {Shi}(a+b x) \, dx=\int x^{m} \operatorname {Shi}{\left (a + b x \right )}\, dx \]

[In]

integrate(x**m*Shi(b*x+a),x)

[Out]

Integral(x**m*Shi(a + b*x), x)

Maxima [N/A]

Not integrable

Time = 0.21 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.20 \[ \int x^m \text {Shi}(a+b x) \, dx=\int { x^{m} {\rm Shi}\left (b x + a\right ) \,d x } \]

[In]

integrate(x^m*Shi(b*x+a),x, algorithm="maxima")

[Out]

integrate(x^m*Shi(b*x + a), x)

Giac [N/A]

Not integrable

Time = 0.27 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.20 \[ \int x^m \text {Shi}(a+b x) \, dx=\int { x^{m} {\rm Shi}\left (b x + a\right ) \,d x } \]

[In]

integrate(x^m*Shi(b*x+a),x, algorithm="giac")

[Out]

integrate(x^m*Shi(b*x + a), x)

Mupad [N/A]

Not integrable

Time = 4.85 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.20 \[ \int x^m \text {Shi}(a+b x) \, dx=\int x^m\,\mathrm {sinhint}\left (a+b\,x\right ) \,d x \]

[In]

int(x^m*sinhint(a + b*x),x)

[Out]

int(x^m*sinhint(a + b*x), x)