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

Optimal. Leaf size=10 \[ \text{Unintegrable}\left (\frac{x}{\tan ^{-1}(a x)^2},x\right ) \]

[Out]

Unintegrable[x/ArcTan[a*x]^2, x]

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Rubi [A]  time = 0.0075483, 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 = {} \[ \int \frac{x}{\tan ^{-1}(a x)^2} \, dx \]

Verification is Not applicable to the result.

[In]

Int[x/ArcTan[a*x]^2,x]

[Out]

Defer[Int][x/ArcTan[a*x]^2, x]

Rubi steps

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

Mathematica [A]  time = 0.590724, size = 0, normalized size = 0. \[ \int \frac{x}{\tan ^{-1}(a x)^2} \, dx \]

Verification is Not applicable to the result.

[In]

Integrate[x/ArcTan[a*x]^2,x]

[Out]

Integrate[x/ArcTan[a*x]^2, x]

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Maple [A]  time = 0.368, size = 0, normalized size = 0. \begin{align*} \int{\frac{x}{ \left ( \arctan \left ( ax \right ) \right ) ^{2}}}\, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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Maxima [A]  time = 0., size = 0, normalized size = 0. \begin{align*} -\frac{a^{2} x^{3} - \arctan \left (a x\right ) \int \frac{3 \, a^{2} x^{2} + 1}{\arctan \left (a x\right )}\,{d x} + x}{a \arctan \left (a x\right )} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-(a^2*x^3 - arctan(a*x)*integrate((3*a^2*x^2 + 1)/arctan(a*x), x) + x)/(a*arctan(a*x))

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

integral(x/arctan(a*x)^2, x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

Integral(x/atan(a*x)**2, x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

integrate(x/arctan(a*x)^2, x)