Optimal. Leaf size=14 \[ \text{Unintegrable}\left (\frac{1}{x \sinh ^{-1}(a+b x)^2},x\right ) \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0386165, antiderivative size = 0, normalized size of antiderivative = 0., number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0., Rules used = {} \[ \int \frac{1}{x \sinh ^{-1}(a+b x)^2} \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
Rubi steps
\begin{align*} \int \frac{1}{x \sinh ^{-1}(a+b x)^2} \, dx &=\frac{\operatorname{Subst}\left (\int \frac{1}{\left (-\frac{a}{b}+\frac{x}{b}\right ) \sinh ^{-1}(x)^2} \, dx,x,a+b x\right )}{b}\\ \end{align*}
Mathematica [A] time = 2.04346, size = 0, normalized size = 0. \[ \int \frac{1}{x \sinh ^{-1}(a+b x)^2} \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.088, size = 0, normalized size = 0. \begin{align*} \int{\frac{1}{x \left ({\it Arcsinh} \left ( bx+a \right ) \right ) ^{2}}}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 0., size = 0, normalized size = 0. \begin{align*} -\frac{b^{3} x^{3} + 3 \, a b^{2} x^{2} + a^{3} +{\left (3 \, a^{2} b + b\right )} x +{\left (b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right )}^{\frac{3}{2}} + a}{{\left (b^{3} x^{3} + 2 \, a b^{2} x^{2} +{\left (a^{2} b + b\right )} x + \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}{\left (b^{2} x^{2} + a b x\right )}\right )} \log \left (b x + a + \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}\right )} - \int \frac{a b^{4} x^{4} + 4 \, a^{2} b^{3} x^{3} + a^{5} + 2 \, a^{3} + 2 \,{\left (3 \, a^{3} b^{2} + a b^{2}\right )} x^{2} +{\left (a b^{2} x^{2} + a^{3} + 2 \,{\left (a^{2} b + b\right )} x + a\right )}{\left (b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right )} + 4 \,{\left (a^{4} b + a^{2} b\right )} x +{\left (2 \, a b^{3} x^{3} + 2 \, a^{4} + 2 \,{\left (3 \, a^{2} b^{2} + b^{2}\right )} x^{2} + 3 \, a^{2} +{\left (6 \, a^{3} b + 5 \, a b\right )} x + 1\right )} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} + a}{{\left (b^{5} x^{6} + 4 \, a b^{4} x^{5} + 2 \,{\left (3 \, a^{2} b^{3} + b^{3}\right )} x^{4} + 4 \,{\left (a^{3} b^{2} + a b^{2}\right )} x^{3} +{\left (a^{4} b + 2 \, a^{2} b + b\right )} x^{2} +{\left (b^{3} x^{4} + 2 \, a b^{2} x^{3} + a^{2} b x^{2}\right )}{\left (b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right )} + 2 \,{\left (b^{4} x^{5} + 3 \, a b^{3} x^{4} +{\left (3 \, a^{2} b^{2} + b^{2}\right )} x^{3} +{\left (a^{3} b + a b\right )} x^{2}\right )} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}\right )} \log \left (b x + a + \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}\right )}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 0., size = 0, normalized size = 0. \begin{align*}{\rm integral}\left (\frac{1}{x \operatorname{arsinh}\left (b x + a\right )^{2}}, x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{1}{x \operatorname{asinh}^{2}{\left (a + b x \right )}}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{1}{x \operatorname{arsinh}\left (b x + a\right )^{2}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]