3.1.58 \(\int (a+b \text {ArcTan}(c x))^p \, dx\) [58]

Optimal. Leaf size=13 \[ \text {Int}\left ((a+b \text {ArcTan}(c x))^p,x\right ) \]

[Out]

Unintegrable((a+b*arctan(c*x))^p,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 (a+b \text {ArcTan}(c x))^p \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(a + b*ArcTan[c*x])^p,x]

[Out]

Defer[Int][(a + b*ArcTan[c*x])^p, x]

Rubi steps

\begin {align*} \int \left (a+b \tan ^{-1}(c x)\right )^p \, dx &=\int \left (a+b \tan ^{-1}(c x)\right )^p \, dx\\ \end {align*}

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Mathematica [A]
time = 0.34, size = 0, normalized size = 0.00 \begin {gather*} \int (a+b \text {ArcTan}(c x))^p \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Integrate[(a + b*ArcTan[c*x])^p,x]

[Out]

Integrate[(a + b*ArcTan[c*x])^p, x]

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Maple [A]
time = 0.49, size = 0, normalized size = 0.00 \[\int \left (a +b \arctan \left (c x \right )\right )^{p}\, dx\]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((a+b*arctan(c*x))^p,x)

[Out]

int((a+b*arctan(c*x))^p,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((a+b*arctan(c*x))^p,x, algorithm="maxima")

[Out]

integrate((b*arctan(c*x) + a)^p, 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((a+b*arctan(c*x))^p,x, algorithm="fricas")

[Out]

integral((b*arctan(c*x) + a)^p, x)

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Sympy [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \left (a + b \operatorname {atan}{\left (c x \right )}\right )^{p}\, dx \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((a+b*atan(c*x))**p,x)

[Out]

Integral((a + b*atan(c*x))**p, 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((a+b*arctan(c*x))^p,x, algorithm="giac")

[Out]

sage0*x

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Mupad [A]
time = 0.00, size = -1, normalized size = -0.08 \begin {gather*} \int {\left (a+b\,\mathrm {atan}\left (c\,x\right )\right )}^p \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((a + b*atan(c*x))^p,x)

[Out]

int((a + b*atan(c*x))^p, x)

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