3.39 \(\int \frac {1}{\tan ^{-1}(a x)^2} \, dx\)

Optimal. Leaf size=9 \[ \text {Int}\left (\frac {1}{\tan ^{-1}(a x)^2},x\right ) \]

[Out]

Unintegrable(1/arctan(a*x)^2,x)

________________________________________________________________________________________

Rubi [A]  time = 0.00, 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 = {} \[ \int \frac {1}{\tan ^{-1}(a x)^2} \, dx \]

Verification is Not applicable to the result.

[In]

Int[ArcTan[a*x]^(-2),x]

[Out]

Defer[Int][ArcTan[a*x]^(-2), x]

Rubi steps

\begin {align*} \int \frac {1}{\tan ^{-1}(a x)^2} \, dx &=\int \frac {1}{\tan ^{-1}(a x)^2} \, dx\\ \end {align*}

________________________________________________________________________________________

Mathematica [A]  time = 0.91, size = 0, normalized size = 0.00 \[ \int \frac {1}{\tan ^{-1}(a x)^2} \, dx \]

Verification is Not applicable to the result.

[In]

Integrate[ArcTan[a*x]^(-2),x]

[Out]

Integrate[ArcTan[a*x]^(-2), x]

________________________________________________________________________________________

fricas [A]  time = 0.42, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {1}{\arctan \left (a x\right )^{2}}, x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/arctan(a*x)^2,x, algorithm="fricas")

[Out]

integral(arctan(a*x)^(-2), x)

________________________________________________________________________________________

giac [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \mathit {sage}_{0} x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/arctan(a*x)^2,x, algorithm="giac")

[Out]

sage0*x

________________________________________________________________________________________

maple [A]  time = 0.26, size = 0, normalized size = 0.00 \[ \int \frac {1}{\arctan \left (a x \right )^{2}}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/arctan(a*x)^2,x)

[Out]

int(1/arctan(a*x)^2,x)

________________________________________________________________________________________

maxima [A]  time = 0.00, size = 0, normalized size = 0.00 \[ -\frac {-2 \, a^{2} \mathit {sage}_{0} x \arctan \left (a x\right ) + a^{2} x^{2} + 1}{a \arctan \left (a x\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/arctan(a*x)^2,x, algorithm="maxima")

[Out]

-(a^2*x^2 - 2*a^2*arctan(a*x)*integrate(x/arctan(a*x), x) + 1)/(a*arctan(a*x))

________________________________________________________________________________________

mupad [A]  time = 0.00, size = -1, normalized size = -0.11 \[ \int \frac {1}{{\mathrm {atan}\left (a\,x\right )}^2} \,d x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/atan(a*x)^2,x)

[Out]

int(1/atan(a*x)^2, x)

________________________________________________________________________________________

sympy [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {1}{\operatorname {atan}^{2}{\left (a x \right )}}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/atan(a*x)**2,x)

[Out]

Integral(atan(a*x)**(-2), x)

________________________________________________________________________________________