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

Optimal. Leaf size=8 \[ \text{Unintegrable}\left (\frac{1}{\tan ^{-1}(a x)^2},x\right ) \]

[Out]

Unintegrable[ArcTan[a*x]^(-2), x]

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Rubi [A]  time = 0.0032723, 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 = {} \[ \int \frac{1}{\tan ^{-1}(a x)^2} \, dx \]

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 = 0.880677, size = 0, normalized size = 0. \[ \int \frac{1}{\tan ^{-1}(a x)^2} \, dx \]

Verification is Not applicable to the result.

[In]

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

[Out]

Integrate[ArcTan[a*x]^(-2), x]

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Maple [A]  time = 0.149, size = 0, normalized size = 0. \begin{align*} \int \left ( \arctan \left ( ax \right ) \right ) ^{-2}\, dx \end{align*}

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)

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Maxima [A]  time = 0., size = 0, normalized size = 0. \begin{align*} -\frac{a^{2} x^{2} - 2 \, a^{2} \arctan \left (a x\right ) \int \frac{x}{\arctan \left (a x\right )}\,{d x} + 1}{a \arctan \left (a x\right )} \end{align*}

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))

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Fricas [A]  time = 0., size = 0, normalized size = 0. \begin{align*}{\rm integral}\left (\frac{1}{\arctan \left (a x\right )^{2}}, x\right ) \end{align*}

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)

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Sympy [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{1}{\operatorname{atan}^{2}{\left (a x \right )}}\, dx \end{align*}

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)

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Giac [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{1}{\arctan \left (a x\right )^{2}}\,{d x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

integrate(arctan(a*x)^(-2), x)