Optimal. Leaf size=29 \[ \text {Int}\left (\frac {\text {csch}^3(a+b x)}{x},x\right )+\text {Int}\left (\frac {\text {csch}(a+b x)}{x},x\right ) \]
[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 = {} \[ \int \frac {\coth ^2(a+b x) \text {csch}(a+b x)}{x} \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
Rubi steps
\begin {align*} \int \frac {\coth ^2(a+b x) \text {csch}(a+b x)}{x} \, dx &=\int \frac {\text {csch}(a+b x)}{x} \, dx+\int \frac {\text {csch}^3(a+b x)}{x} \, dx\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 54.01, size = 0, normalized size = 0.00 \[ \int \frac {\coth ^2(a+b x) \text {csch}(a+b x)}{x} \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.42, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {\cosh \left (b x + a\right )^{2} \operatorname {csch}\left (b x + a\right )^{3}}{x}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {\cosh \left (b x + a\right )^{2} \operatorname {csch}\left (b x + a\right )^{3}}{x}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.92, size = 0, normalized size = 0.00 \[ \int \frac {\left (\cosh ^{2}\left (b x +a \right )\right ) \mathrm {csch}\left (b x +a \right )^{3}}{x}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.00, size = 0, normalized size = 0.00 \[ -\frac {{\left (b x e^{\left (3 \, a\right )} - e^{\left (3 \, a\right )}\right )} e^{\left (3 \, b x\right )} + {\left (b x e^{a} + e^{a}\right )} e^{\left (b x\right )}}{b^{2} x^{2} e^{\left (4 \, b x + 4 \, a\right )} - 2 \, b^{2} x^{2} e^{\left (2 \, b x + 2 \, a\right )} + b^{2} x^{2}} + 2 \, \int \frac {b^{2} x^{2} + 2}{4 \, {\left (b^{2} x^{3} e^{\left (b x + a\right )} + b^{2} x^{3}\right )}}\,{d x} + 2 \, \int \frac {b^{2} x^{2} + 2}{4 \, {\left (b^{2} x^{3} e^{\left (b x + a\right )} - b^{2} x^{3}\right )}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [A] time = 0.00, size = -1, normalized size = -0.03 \[ \int \frac {{\mathrm {cosh}\left (a+b\,x\right )}^2}{x\,{\mathrm {sinh}\left (a+b\,x\right )}^3} \,d x \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {\cosh ^{2}{\left (a + b x \right )} \operatorname {csch}^{3}{\left (a + b x \right )}}{x}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________