\(\int \frac {e^{\text {arcsinh}(a+b x)^2}}{x^2} \, dx\) [363]

Optimal result

Integrand size = 14, antiderivative size = 14 \[ \int \frac {e^{\text {arcsinh}(a+b x)^2}}{x^2} \, dx=\text {Int}\left (\frac {e^{\text {arcsinh}(a+b x)^2}}{x^2},x\right ) \]

[Out]

CannotIntegrate(exp(arcsinh(b*x+a)^2)/x^2,x)

Rubi [N/A]

Not integrable

Time = 0.03 (sec) , antiderivative size = 14, 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 = {} \[ \int \frac {e^{\text {arcsinh}(a+b x)^2}}{x^2} \, dx=\int \frac {e^{\text {arcsinh}(a+b x)^2}}{x^2} \, dx \]

[In]

Int[E^ArcSinh[a + b*x]^2/x^2,x]

[Out]

Defer[Int][E^ArcSinh[a + b*x]^2/x^2, x]

Rubi steps \begin{align*} \text {integral}& = \int \frac {e^{\text {arcsinh}(a+b x)^2}}{x^2} \, dx \\ \end{align*}

Mathematica [N/A]

Not integrable

Time = 0.34 (sec) , antiderivative size = 16, normalized size of antiderivative = 1.14 \[ \int \frac {e^{\text {arcsinh}(a+b x)^2}}{x^2} \, dx=\int \frac {e^{\text {arcsinh}(a+b x)^2}}{x^2} \, dx \]

[In]

Integrate[E^ArcSinh[a + b*x]^2/x^2,x]

[Out]

Integrate[E^ArcSinh[a + b*x]^2/x^2, x]

Maple [N/A] (verified)

Not integrable

Time = 0.01 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.93

\[\int \frac {{\mathrm e}^{\operatorname {arcsinh}\left (b x +a \right )^{2}}}{x^{2}}d x\]

[In]

int(exp(arcsinh(b*x+a)^2)/x^2,x)

[Out]

int(exp(arcsinh(b*x+a)^2)/x^2,x)

Fricas [N/A]

Not integrable

Time = 0.26 (sec) , antiderivative size = 15, normalized size of antiderivative = 1.07 \[ \int \frac {e^{\text {arcsinh}(a+b x)^2}}{x^2} \, dx=\int { \frac {e^{\left (\operatorname {arsinh}\left (b x + a\right )^{2}\right )}}{x^{2}} \,d x } \]

[In]

integrate(exp(arcsinh(b*x+a)^2)/x^2,x, algorithm="fricas")

[Out]

integral(e^(arcsinh(b*x + a)^2)/x^2, x)

Sympy [N/A]

Not integrable

Time = 0.39 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.00 \[ \int \frac {e^{\text {arcsinh}(a+b x)^2}}{x^2} \, dx=\int \frac {e^{\operatorname {asinh}^{2}{\left (a + b x \right )}}}{x^{2}}\, dx \]

[In]

integrate(exp(asinh(b*x+a)**2)/x**2,x)

[Out]

Integral(exp(asinh(a + b*x)**2)/x**2, x)

Maxima [N/A]

Not integrable

Time = 0.45 (sec) , antiderivative size = 15, normalized size of antiderivative = 1.07 \[ \int \frac {e^{\text {arcsinh}(a+b x)^2}}{x^2} \, dx=\int { \frac {e^{\left (\operatorname {arsinh}\left (b x + a\right )^{2}\right )}}{x^{2}} \,d x } \]

[In]

integrate(exp(arcsinh(b*x+a)^2)/x^2,x, algorithm="maxima")

[Out]

integrate(e^(arcsinh(b*x + a)^2)/x^2, x)

Giac [N/A]

Not integrable

Time = 0.33 (sec) , antiderivative size = 15, normalized size of antiderivative = 1.07 \[ \int \frac {e^{\text {arcsinh}(a+b x)^2}}{x^2} \, dx=\int { \frac {e^{\left (\operatorname {arsinh}\left (b x + a\right )^{2}\right )}}{x^{2}} \,d x } \]

[In]

integrate(exp(arcsinh(b*x+a)^2)/x^2,x, algorithm="giac")

[Out]

integrate(e^(arcsinh(b*x + a)^2)/x^2, x)

Mupad [N/A]

Not integrable

Time = 2.57 (sec) , antiderivative size = 15, normalized size of antiderivative = 1.07 \[ \int \frac {e^{\text {arcsinh}(a+b x)^2}}{x^2} \, dx=\int \frac {{\mathrm {e}}^{{\mathrm {asinh}\left (a+b\,x\right )}^2}}{x^2} \,d x \]

[In]

int(exp(asinh(a + b*x)^2)/x^2,x)

[Out]

int(exp(asinh(a + b*x)^2)/x^2, x)