3.5.66 \(\int \frac {x (c+a^2 c x^2)}{\text {ArcTan}(a x)} \, dx\) [466]

Optimal. Leaf size=21 \[ \text {Int}\left (\frac {x \left (c+a^2 c x^2\right )}{\text {ArcTan}(a x)},x\right ) \]

[Out]

Unintegrable(x*(a^2*c*x^2+c)/arctan(a*x),x)

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Rubi [A]
time = 0.02, 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 \frac {x \left (c+a^2 c x^2\right )}{\text {ArcTan}(a x)} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(x*(c + a^2*c*x^2))/ArcTan[a*x],x]

[Out]

Defer[Int][(x*(c + a^2*c*x^2))/ArcTan[a*x], x]

Rubi steps

\begin {align*} \int \frac {x \left (c+a^2 c x^2\right )}{\tan ^{-1}(a x)} \, dx &=\int \frac {x \left (c+a^2 c x^2\right )}{\tan ^{-1}(a x)} \, dx\\ \end {align*}

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Mathematica [A]
time = 0.30, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {x \left (c+a^2 c x^2\right )}{\text {ArcTan}(a x)} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Integrate[(x*(c + a^2*c*x^2))/ArcTan[a*x],x]

[Out]

Integrate[(x*(c + a^2*c*x^2))/ArcTan[a*x], x]

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Maple [A]
time = 15.57, size = 0, normalized size = 0.00 \[\int \frac {x \left (a^{2} c \,x^{2}+c \right )}{\arctan \left (a x \right )}\, dx\]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(x*(a^2*c*x^2+c)/arctan(a*x),x)

[Out]

int(x*(a^2*c*x^2+c)/arctan(a*x),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*(a^2*c*x^2+c)/arctan(a*x),x, algorithm="maxima")

[Out]

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

[Out]

integral((a^2*c*x^3 + c*x)/arctan(a*x), x)

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Sympy [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} c \left (\int \frac {x}{\operatorname {atan}{\left (a x \right )}}\, dx + \int \frac {a^{2} x^{3}}{\operatorname {atan}{\left (a x \right )}}\, dx\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(x*(a**2*c*x**2+c)/atan(a*x),x)

[Out]

c*(Integral(x/atan(a*x), x) + Integral(a**2*x**3/atan(a*x), 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*(a^2*c*x^2+c)/arctan(a*x),x, algorithm="giac")

[Out]

sage0*x

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Mupad [A]
time = 0.00, size = -1, normalized size = -0.05 \begin {gather*} \int \frac {x\,\left (c\,a^2\,x^2+c\right )}{\mathrm {atan}\left (a\,x\right )} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((x*(c + a^2*c*x^2))/atan(a*x),x)

[Out]

int((x*(c + a^2*c*x^2))/atan(a*x), x)

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