Optimal. Leaf size=27 \[ \frac {\text {Int}\left (\frac {1}{(c+d x) \left (a+b \cosh ^{-1}(c+d x)\right )},x\right )}{e} \]
[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 = {} \[ \int \frac {1}{(c e+d e x) \left (a+b \cosh ^{-1}(c+d x)\right )} \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
Rubi steps
\begin {align*} \int \frac {1}{(c e+d e x) \left (a+b \cosh ^{-1}(c+d x)\right )} \, dx &=\frac {\operatorname {Subst}\left (\int \frac {1}{e x \left (a+b \cosh ^{-1}(x)\right )} \, dx,x,c+d x\right )}{d}\\ &=\frac {\operatorname {Subst}\left (\int \frac {1}{x \left (a+b \cosh ^{-1}(x)\right )} \, dx,x,c+d x\right )}{d e}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.88, size = 0, normalized size = 0.00 \[ \int \frac {1}{(c e+d e x) \left (a+b \cosh ^{-1}(c+d x)\right )} \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.68, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {1}{a d e x + a c e + {\left (b d e x + b c e\right )} \operatorname {arcosh}\left (d x + c\right )}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {1}{{\left (d e x + c e\right )} {\left (b \operatorname {arcosh}\left (d x + c\right ) + a\right )}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.26, size = 0, normalized size = 0.00 \[ \int \frac {1}{\left (d e x +c e \right ) \left (a +b \,\mathrm {arccosh}\left (d x +c \right )\right )}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {1}{{\left (d e x + c e\right )} {\left (b \operatorname {arcosh}\left (d x + c\right ) + a\right )}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [A] time = 0.00, size = -1, normalized size = -0.04 \[ \int \frac {1}{\left (c\,e+d\,e\,x\right )\,\left (a+b\,\mathrm {acosh}\left (c+d\,x\right )\right )} \,d x \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.00, size = 0, normalized size = 0.00 \[ \frac {\int \frac {1}{a c + a d x + b c \operatorname {acosh}{\left (c + d x \right )} + b d x \operatorname {acosh}{\left (c + d x \right )}}\, dx}{e} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________