Optimal. Leaf size=25 \[ \text {Int}\left (\frac {1}{\left (d+e x^2\right ) \sqrt {a+b \cosh ^{-1}(c x)}},x\right ) \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.06, 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 = {} \[ \int \frac {1}{\left (d+e x^2\right ) \sqrt {a+b \cosh ^{-1}(c x)}} \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
Rubi steps
\begin {align*} \int \frac {1}{\left (d+e x^2\right ) \sqrt {a+b \cosh ^{-1}(c x)}} \, dx &=\int \frac {1}{\left (d+e x^2\right ) \sqrt {a+b \cosh ^{-1}(c x)}} \, dx\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.16, size = 0, normalized size = 0.00 \[ \int \frac {1}{\left (d+e x^2\right ) \sqrt {a+b \cosh ^{-1}(c x)}} \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
________________________________________________________________________________________
fricas [F(-2)] time = 0.00, size = 0, normalized size = 0.00 \[ \text {Exception raised: TypeError} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {1}{{\left (e x^{2} + d\right )} \sqrt {b \operatorname {arcosh}\left (c x\right ) + a}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.64, size = 0, normalized size = 0.00 \[ \int \frac {1}{\left (e \,x^{2}+d \right ) \sqrt {a +b \,\mathrm {arccosh}\left (c x \right )}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {1}{{\left (e x^{2} + d\right )} \sqrt {b \operatorname {arcosh}\left (c x\right ) + a}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [A] time = 0.00, size = -1, normalized size = -0.04 \[ \int \frac {1}{\sqrt {a+b\,\mathrm {acosh}\left (c\,x\right )}\,\left (e\,x^2+d\right )} \,d x \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {1}{\sqrt {a + b \operatorname {acosh}{\left (c x \right )}} \left (d + e x^{2}\right )}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________