Optimal. Leaf size=19 \[ \text {Int}\left (\frac {\cot ^{-1}(a x)}{\sqrt {c+d x^2}},x\right ) \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.02, 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 = {} \[ \int \frac {\cot ^{-1}(a x)}{\sqrt {c+d x^2}} \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
Rubi steps
\begin {align*} \int \frac {\cot ^{-1}(a x)}{\sqrt {c+d x^2}} \, dx &=\int \frac {\cot ^{-1}(a x)}{\sqrt {c+d x^2}} \, dx\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 4.23, size = 0, normalized size = 0.00 \[ \int \frac {\cot ^{-1}(a x)}{\sqrt {c+d x^2}} \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.96, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {\operatorname {arccot}\left (a x\right )}{\sqrt {d x^{2} + c}}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {\operatorname {arccot}\left (a x\right )}{\sqrt {d x^{2} + c}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 1.29, size = 0, normalized size = 0.00 \[ \int \frac {\mathrm {arccot}\left (a x \right )}{\sqrt {d \,x^{2}+c}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {\operatorname {arccot}\left (a x\right )}{\sqrt {d x^{2} + c}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [A] time = 0.00, size = -1, normalized size = -0.05 \[ \int \frac {\mathrm {acot}\left (a\,x\right )}{\sqrt {d\,x^2+c}} \,d x \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {\operatorname {acot}{\left (a x \right )}}{\sqrt {c + d x^{2}}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________