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

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

[Out]

Unintegrable[ArcTan[a*x]^(-1), x]

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Rubi [A]  time = 0.0032902, 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 = {} \[ \int \frac{1}{\tan ^{-1}(a x)} \, dx \]

Verification is Not applicable to the result.

[In]

Int[ArcTan[a*x]^(-1),x]

[Out]

Defer[Int][ArcTan[a*x]^(-1), x]

Rubi steps

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

Mathematica [A]  time = 0.0109886, size = 0, normalized size = 0. \[ \int \frac{1}{\tan ^{-1}(a x)} \, dx \]

Verification is Not applicable to the result.

[In]

Integrate[ArcTan[a*x]^(-1),x]

[Out]

Integrate[ArcTan[a*x]^(-1), x]

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Maple [A]  time = 0.148, size = 0, normalized size = 0. \begin{align*} \int \left ( \arctan \left ( ax \right ) \right ) ^{-1}\, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

integrate(1/arctan(a*x), 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 )}, x\right ) \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

integral(1/arctan(a*x), x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

Integral(1/atan(a*x), x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

integrate(1/arctan(a*x), x)