Integrand size = 12, antiderivative size = 12 \[ \int x^m \text {Shi}(a+b x)^2 \, dx=\text {Int}\left (x^m \text {Shi}(a+b x)^2,x\right ) \]
[Out]
Not integrable
Time = 0.03 (sec) , antiderivative size = 12, 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 = {} \[ \int x^m \text {Shi}(a+b x)^2 \, dx=\int x^m \text {Shi}(a+b x)^2 \, dx \]
[In]
[Out]
Rubi steps \begin{align*} \text {integral}& = \int x^m \text {Shi}(a+b x)^2 \, dx \\ \end{align*}
Not integrable
Time = 4.58 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.17 \[ \int x^m \text {Shi}(a+b x)^2 \, dx=\int x^m \text {Shi}(a+b x)^2 \, dx \]
[In]
[Out]
Not integrable
Time = 0.22 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.00
\[\int x^{m} \operatorname {Shi}\left (b x +a \right )^{2}d x\]
[In]
[Out]
Not integrable
Time = 0.27 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.17 \[ \int x^m \text {Shi}(a+b x)^2 \, dx=\int { x^{m} {\rm Shi}\left (b x + a\right )^{2} \,d x } \]
[In]
[Out]
Not integrable
Time = 1.14 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.00 \[ \int x^m \text {Shi}(a+b x)^2 \, dx=\int x^{m} \operatorname {Shi}^{2}{\left (a + b x \right )}\, dx \]
[In]
[Out]
Not integrable
Time = 0.23 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.17 \[ \int x^m \text {Shi}(a+b x)^2 \, dx=\int { x^{m} {\rm Shi}\left (b x + a\right )^{2} \,d x } \]
[In]
[Out]
Not integrable
Time = 0.28 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.17 \[ \int x^m \text {Shi}(a+b x)^2 \, dx=\int { x^{m} {\rm Shi}\left (b x + a\right )^{2} \,d x } \]
[In]
[Out]
Not integrable
Time = 4.90 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.17 \[ \int x^m \text {Shi}(a+b x)^2 \, dx=\int x^m\,{\mathrm {sinhint}\left (a+b\,x\right )}^2 \,d x \]
[In]
[Out]