3.41 \(\int x \sqrt{\tan ^{-1}(a x)} \, dx\)

Optimal. Leaf size=12 \[ \text{Unintegrable}\left (x \sqrt{\tan ^{-1}(a x)},x\right ) \]

[Out]

Unintegrable[x*Sqrt[ArcTan[a*x]], x]

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Rubi [A]  time = 0.0073851, 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 = {} \[ \int x \sqrt{\tan ^{-1}(a x)} \, dx \]

Verification is Not applicable to the result.

[In]

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

[Out]

Defer[Int][x*Sqrt[ArcTan[a*x]], x]

Rubi steps

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

Mathematica [A]  time = 1.95853, size = 0, normalized size = 0. \[ \int x \sqrt{\tan ^{-1}(a x)} \, dx \]

Verification is Not applicable to the result.

[In]

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

[Out]

Integrate[x*Sqrt[ArcTan[a*x]], x]

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Maple [A]  time = 0.246, size = 0, normalized size = 0. \begin{align*} \int x\sqrt{\arctan \left ( ax \right ) }\, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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Maxima [F(-2)]  time = 0., size = 0, normalized size = 0. \begin{align*} \text{Exception raised: RuntimeError} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

Exception raised: RuntimeError

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Fricas [F(-2)]  time = 0., size = 0, normalized size = 0. \begin{align*} \text{Exception raised: UnboundLocalError} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

Exception raised: UnboundLocalError

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(x*atan(a*x)**(1/2),x)

[Out]

Integral(x*sqrt(atan(a*x)), x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

integrate(x*sqrt(arctan(a*x)), x)