Optimal. Leaf size=21 \[ \text {Int}\left (\frac {\left (a+b \text {csch}\left (c+d x^2\right )\right )^2}{x^2},x\right ) \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.03, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \[ \int \frac {\left (a+b \text {csch}\left (c+d x^2\right )\right )^2}{x^2} \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
Rubi steps
\begin {align*} \int \frac {\left (a+b \text {csch}\left (c+d x^2\right )\right )^2}{x^2} \, dx &=\int \frac {\left (a+b \text {csch}\left (c+d x^2\right )\right )^2}{x^2} \, dx\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 43.91, size = 0, normalized size = 0.00 \[ \int \frac {\left (a+b \text {csch}\left (c+d x^2\right )\right )^2}{x^2} \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.41, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {b^{2} \operatorname {csch}\left (d x^{2} + c\right )^{2} + 2 \, a b \operatorname {csch}\left (d x^{2} + c\right ) + a^{2}}{x^{2}}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {{\left (b \operatorname {csch}\left (d x^{2} + c\right ) + a\right )}^{2}}{x^{2}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.46, size = 0, normalized size = 0.00 \[ \int \frac {\left (a +b \,\mathrm {csch}\left (d \,x^{2}+c \right )\right )^{2}}{x^{2}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.00, size = 0, normalized size = 0.00 \[ -\frac {b^{2}}{d x^{3} e^{\left (2 \, d x^{2} + 2 \, c\right )} - d x^{3}} - \frac {a^{2}}{x} + \int \frac {4 \, a b d x^{2} + 3 \, b^{2}}{2 \, {\left (d x^{4} e^{\left (d x^{2} + c\right )} + d x^{4}\right )}}\,{d x} + \int \frac {4 \, a b d x^{2} - 3 \, b^{2}}{2 \, {\left (d x^{4} e^{\left (d x^{2} + c\right )} - d x^{4}\right )}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [A] time = 0.00, size = -1, normalized size = -0.05 \[ \int \frac {{\left (a+\frac {b}{\mathrm {sinh}\left (d\,x^2+c\right )}\right )}^2}{x^2} \,d x \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {\left (a + b \operatorname {csch}{\left (c + d x^{2} \right )}\right )^{2}}{x^{2}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________