Optimal. Leaf size=20 \[ 4 \text {Int}\left (\frac {\text {csch}^2(2 a+2 b x)}{x^2},x\right ) \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.07, 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 = {} \[ \int \frac {\text {csch}^2(a+b x) \text {sech}^2(a+b x)}{x^2} \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
Rubi steps
\begin {align*} \int \frac {\text {csch}^2(a+b x) \text {sech}^2(a+b x)}{x^2} \, dx &=4 \int \frac {\text {csch}^2(2 a+2 b x)}{x^2} \, dx\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 21.12, size = 0, normalized size = 0.00 \[ \int \frac {\text {csch}^2(a+b x) \text {sech}^2(a+b x)}{x^2} \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.41, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {\operatorname {csch}\left (b x + a\right )^{2} \operatorname {sech}\left (b x + a\right )^{2}}{x^{2}}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {\operatorname {csch}\left (b x + a\right )^{2} \operatorname {sech}\left (b x + a\right )^{2}}{x^{2}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.53, size = 0, normalized size = 0.00 \[ \int \frac {\mathrm {csch}\left (b x +a \right )^{2} \mathrm {sech}\left (b x +a \right )^{2}}{x^{2}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.00, size = 0, normalized size = 0.00 \[ -\frac {4}{b x^{2} e^{\left (4 \, b x + 4 \, a\right )} - b x^{2}} + 16 \, \int \frac {1}{4 \, {\left (b x^{3} e^{\left (2 \, b x + 2 \, a\right )} + b x^{3}\right )}}\,{d x} + 16 \, \int \frac {1}{8 \, {\left (b x^{3} e^{\left (b x + a\right )} + b x^{3}\right )}}\,{d x} - 16 \, \int \frac {1}{8 \, {\left (b x^{3} e^{\left (b x + a\right )} - b x^{3}\right )}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [A] time = 0.00, size = -1, normalized size = -0.05 \[ \int \frac {1}{x^2\,{\mathrm {cosh}\left (a+b\,x\right )}^2\,{\mathrm {sinh}\left (a+b\,x\right )}^2} \,d x \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {\operatorname {csch}^{2}{\left (a + b x \right )} \operatorname {sech}^{2}{\left (a + b x \right )}}{x^{2}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________