\(\int x^m \text {Shi}(b x)^2 \, dx\) [9]

Optimal result

Integrand size = 10, antiderivative size = 10 \[ \int x^m \text {Shi}(b x)^2 \, dx=\text {Int}\left (x^m \text {Shi}(b x)^2,x\right ) \]

[Out]

CannotIntegrate(x^m*Shi(b*x)^2,x)

Rubi [N/A]

Not integrable

Time = 0.02 (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 = {} \[ \int x^m \text {Shi}(b x)^2 \, dx=\int x^m \text {Shi}(b x)^2 \, dx \]

[In]

Int[x^m*SinhIntegral[b*x]^2,x]

[Out]

Defer[Int][x^m*SinhIntegral[b*x]^2, x]

Rubi steps \begin{align*} \text {integral}& = \int x^m \text {Shi}(b x)^2 \, dx \\ \end{align*}

Mathematica [N/A]

Not integrable

Time = 0.45 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.20 \[ \int x^m \text {Shi}(b x)^2 \, dx=\int x^m \text {Shi}(b x)^2 \, dx \]

[In]

Integrate[x^m*SinhIntegral[b*x]^2,x]

[Out]

Integrate[x^m*SinhIntegral[b*x]^2, x]

Maple [N/A] (verified)

Not integrable

Time = 0.22 (sec) , antiderivative size = 10, normalized size of antiderivative = 1.00

\[\int x^{m} \operatorname {Shi}\left (b x \right )^{2}d x\]

[In]

int(x^m*Shi(b*x)^2,x)

[Out]

int(x^m*Shi(b*x)^2,x)

Fricas [N/A]

Not integrable

Time = 0.24 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.20 \[ \int x^m \text {Shi}(b x)^2 \, dx=\int { x^{m} {\rm Shi}\left (b x\right )^{2} \,d x } \]

[In]

integrate(x^m*Shi(b*x)^2,x, algorithm="fricas")

[Out]

integral(x^m*sinh_integral(b*x)^2, x)

Sympy [N/A]

Not integrable

Time = 1.29 (sec) , antiderivative size = 10, normalized size of antiderivative = 1.00 \[ \int x^m \text {Shi}(b x)^2 \, dx=\int x^{m} \operatorname {Shi}^{2}{\left (b x \right )}\, dx \]

[In]

integrate(x**m*Shi(b*x)**2,x)

[Out]

Integral(x**m*Shi(b*x)**2, x)

Maxima [N/A]

Not integrable

Time = 0.21 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.20 \[ \int x^m \text {Shi}(b x)^2 \, dx=\int { x^{m} {\rm Shi}\left (b x\right )^{2} \,d x } \]

[In]

integrate(x^m*Shi(b*x)^2,x, algorithm="maxima")

[Out]

integrate(x^m*Shi(b*x)^2, x)

Giac [N/A]

Not integrable

Time = 0.27 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.20 \[ \int x^m \text {Shi}(b x)^2 \, dx=\int { x^{m} {\rm Shi}\left (b x\right )^{2} \,d x } \]

[In]

integrate(x^m*Shi(b*x)^2,x, algorithm="giac")

[Out]

integrate(x^m*Shi(b*x)^2, x)

Mupad [N/A]

Not integrable

Time = 4.88 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.20 \[ \int x^m \text {Shi}(b x)^2 \, dx=\int x^m\,{\mathrm {sinhint}\left (b\,x\right )}^2 \,d x \]

[In]

int(x^m*sinhint(b*x)^2,x)

[Out]

int(x^m*sinhint(b*x)^2, x)