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

Optimal. Leaf size=11 \[ \text {Int}\left (\frac {x}{\tan ^{-1}(a x)},x\right ) \]

[Out]

Unintegrable(x/arctan(a*x),x)

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Rubi [A]  time = 0.01, 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 = {} \[ \int \frac {x}{\tan ^{-1}(a x)} \, dx \]

Verification is Not applicable to the result.

[In]

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

[Out]

Defer[Int][x/ArcTan[a*x], x]

Rubi steps

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

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Mathematica [A]  time = 0.65, size = 0, normalized size = 0.00 \[ \int \frac {x}{\tan ^{-1}(a x)} \, dx \]

Verification is Not applicable to the result.

[In]

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

[Out]

Integrate[x/ArcTan[a*x], x]

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

integral(x/arctan(a*x), x)

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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(x/arctan(a*x),x, algorithm="giac")

[Out]

sage0*x

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maple [A]  time = 0.47, size = 0, normalized size = 0.00 \[ \int \frac {x}{\arctan \left (a x \right )}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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maxima [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {x}{\arctan \left (a x\right )}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

integrate(x/arctan(a*x), x)

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mupad [A]  time = 0.00, size = -1, normalized size = -0.09 \[ \int \frac {x}{\mathrm {atan}\left (a\,x\right )} \,d x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(x/atan(a*x),x)

[Out]

int(x/atan(a*x), x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

Integral(x/atan(a*x), x)

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