3.1.39 \(\int \frac {1}{\text {ArcTan}(a x)^2} \, dx\) [39]

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

[Out]

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

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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 = {} \begin {gather*} \int \frac {1}{\text {ArcTan}(a x)^2} \, dx \end {gather*}

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*}

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Mathematica [A]
time = 0.65, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {1}{\text {ArcTan}(a x)^2} \, dx \end {gather*}

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 = 0.46, 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)

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Maxima [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Failed to integrate} \end {gather*}

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 = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}

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 = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {1}{\operatorname {atan}^{2}{\left (a x \right )}}\, dx \end {gather*}

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 = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

sage0*x

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

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)

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