3.128 \(\int (a+b x)^2 \sqrt{\cot ^{-1}(a+b x)} \, dx\)

Optimal. Leaf size=20 \[ \text{Unintegrable}\left ((a+b x)^2 \sqrt{\cot ^{-1}(a+b x)},x\right ) \]

[Out]

Unintegrable[(a + b*x)^2*Sqrt[ArcCot[a + b*x]], x]

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Rubi [A]  time = 0.0176178, 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 = {} \[ \int (a+b x)^2 \sqrt{\cot ^{-1}(a+b x)} \, dx \]

Verification is Not applicable to the result.

[In]

Int[(a + b*x)^2*Sqrt[ArcCot[a + b*x]],x]

[Out]

Defer[Int][(a + b*x)^2*Sqrt[ArcCot[a + b*x]], x]

Rubi steps

\begin{align*} \int (a+b x)^2 \sqrt{\cot ^{-1}(a+b x)} \, dx &=\int (a+b x)^2 \sqrt{\cot ^{-1}(a+b x)} \, dx\\ \end{align*}

Mathematica [A]  time = 8.5454, size = 0, normalized size = 0. \[ \int (a+b x)^2 \sqrt{\cot ^{-1}(a+b x)} \, dx \]

Verification is Not applicable to the result.

[In]

Integrate[(a + b*x)^2*Sqrt[ArcCot[a + b*x]],x]

[Out]

Integrate[(a + b*x)^2*Sqrt[ArcCot[a + b*x]], x]

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Maple [A]  time = 0.55, size = 0, normalized size = 0. \begin{align*} \int \left ( bx+a \right ) ^{2}\sqrt{{\rm arccot} \left (bx+a\right )}\, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((b*x+a)^2*arccot(b*x+a)^(1/2),x)

[Out]

int((b*x+a)^2*arccot(b*x+a)^(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((b*x+a)^2*arccot(b*x+a)^(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((b*x+a)^2*arccot(b*x+a)^(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 \left (a + b x\right )^{2} \sqrt{\operatorname{acot}{\left (a + b x \right )}}\, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((b*x+a)**2*acot(b*x+a)**(1/2),x)

[Out]

Integral((a + b*x)**2*sqrt(acot(a + b*x)), x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((b*x+a)^2*arccot(b*x+a)^(1/2),x, algorithm="giac")

[Out]

integrate((b*x + a)^2*sqrt(arccot(b*x + a)), x)