3.1.35 \(\int x^m \cot ^{-1}(a x)^2 \, dx\) [35]

Optimal. Leaf size=13 \[ \text {Int}\left (x^m \cot ^{-1}(a x)^2,x\right ) \]

[Out]

Unintegrable(x^m*arccot(a*x)^2,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 = {} \begin {gather*} \int x^m \cot ^{-1}(a x)^2 \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[x^m*ArcCot[a*x]^2,x]

[Out]

Defer[Int][x^m*ArcCot[a*x]^2, x]

Rubi steps

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

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Mathematica [A]
time = 0.63, size = 0, normalized size = 0.00 \begin {gather*} \int x^m \cot ^{-1}(a x)^2 \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Integrate[x^m*ArcCot[a*x]^2,x]

[Out]

Integrate[x^m*ArcCot[a*x]^2, x]

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Maple [A]
time = 0.15, size = 0, normalized size = 0.00 \[\int x^{m} \mathrm {arccot}\left (a x \right )^{2}\, dx\]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(x^m*arccot(a*x)^2,x)

[Out]

int(x^m*arccot(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(x^m*arccot(a*x)^2,x, algorithm="maxima")

[Out]

1/16*(4*x*x^m*arctan2(1, a*x)^2 - x*x^m*log(a^2*x^2 + 1)^2 + 16*(m + 1)*integrate(1/16*(4*a^2*x^2*x^m*log(a^2*
x^2 + 1) + ((a^2*m + a^2)*x^2 + m + 1)*x^m*log(a^2*x^2 + 1)^2 + 4*(3*(a^2*m*arctan2(1, a*x)^2 + a^2*arctan2(1,
a*x)^2)*x^2 + 2*a*x*arctan2(1, a*x) + 3*m*arctan2(1, a*x)^2 + 3*arctan2(1, a*x)^2)*x^m)/((a^2*m + a^2)*x^2 +
m + 1), x))/(m + 1)

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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(x^m*arccot(a*x)^2,x, algorithm="fricas")

[Out]

integral(x^m*arccot(a*x)^2, x)

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Sympy [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int x^{m} \operatorname {acot}^{2}{\left (a x \right )}\, dx \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(x**m*acot(a*x)**2,x)

[Out]

Integral(x**m*acot(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(x^m*arccot(a*x)^2,x, algorithm="giac")

[Out]

integrate(x^m*arccot(a*x)^2, x)

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Mupad [A]
time = 0.00, size = -1, normalized size = -0.08 \begin {gather*} \int x^m\,{\mathrm {acot}\left (a\,x\right )}^2 \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(x^m*acot(a*x)^2,x)

[Out]

int(x^m*acot(a*x)^2, x)

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