\(\int \frac {x}{\arctan (a x)^2} \, dx\) [38]

Optimal result

Integrand size = 8, antiderivative size = 8 \[ \int \frac {x}{\arctan (a x)^2} \, dx=\text {Int}\left (\frac {x}{\arctan (a x)^2},x\right ) \]

[Out]

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

Rubi [N/A]

Not integrable

Time = 0.01 (sec) , antiderivative size = 8, normalized size of antiderivative = 1.00, number of steps used = 0, number of rules used = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \[ \int \frac {x}{\arctan (a x)^2} \, dx=\int \frac {x}{\arctan (a x)^2} \, dx \]

[In]

Int[x/ArcTan[a*x]^2,x]

[Out]

Defer[Int][x/ArcTan[a*x]^2, x]

Rubi steps \begin{align*} \text {integral}& = \int \frac {x}{\arctan (a x)^2} \, dx \\ \end{align*}

Mathematica [N/A]

Not integrable

Time = 0.72 (sec) , antiderivative size = 10, normalized size of antiderivative = 1.25 \[ \int \frac {x}{\arctan (a x)^2} \, dx=\int \frac {x}{\arctan (a x)^2} \, dx \]

[In]

Integrate[x/ArcTan[a*x]^2,x]

[Out]

Integrate[x/ArcTan[a*x]^2, x]

Maple [N/A] (verified)

Not integrable

Time = 10.51 (sec) , antiderivative size = 8, normalized size of antiderivative = 1.00

\[\int \frac {x}{\arctan \left (a x \right )^{2}}d x\]

[In]

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

[Out]

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

Fricas [N/A]

Not integrable

Time = 0.23 (sec) , antiderivative size = 10, normalized size of antiderivative = 1.25 \[ \int \frac {x}{\arctan (a x)^2} \, dx=\int { \frac {x}{\arctan \left (a x\right )^{2}} \,d x } \]

[In]

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

[Out]

integral(x/arctan(a*x)^2, x)

Sympy [N/A]

Not integrable

Time = 0.31 (sec) , antiderivative size = 8, normalized size of antiderivative = 1.00 \[ \int \frac {x}{\arctan (a x)^2} \, dx=\int \frac {x}{\operatorname {atan}^{2}{\left (a x \right )}}\, dx \]

[In]

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

[Out]

Integral(x/atan(a*x)**2, x)

Maxima [N/A]

Not integrable

Time = 0.26 (sec) , antiderivative size = 45, normalized size of antiderivative = 5.62 \[ \int \frac {x}{\arctan (a x)^2} \, dx=\int { \frac {x}{\arctan \left (a x\right )^{2}} \,d x } \]

[In]

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

[Out]

-(a^2*x^3 - arctan(a*x)*integrate((3*a^2*x^2 + 1)/arctan(a*x), x) + x)/(a*arctan(a*x))

Giac [N/A]

Not integrable

Time = 49.11 (sec) , antiderivative size = 3, normalized size of antiderivative = 0.38 \[ \int \frac {x}{\arctan (a x)^2} \, dx=\int { \frac {x}{\arctan \left (a x\right )^{2}} \,d x } \]

[In]

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

[Out]

sage0*x

Mupad [N/A]

Not integrable

Time = 0.29 (sec) , antiderivative size = 10, normalized size of antiderivative = 1.25 \[ \int \frac {x}{\arctan (a x)^2} \, dx=\int \frac {x}{{\mathrm {atan}\left (a\,x\right )}^2} \,d x \]

[In]

int(x/atan(a*x)^2,x)

[Out]

int(x/atan(a*x)^2, x)