\(\int \frac {1}{\arctan (a x)} \, dx\) [36]

Optimal result

Integrand size = 6, antiderivative size = 6 \[ \int \frac {1}{\arctan (a x)} \, dx=\text {Int}\left (\frac {1}{\arctan (a x)},x\right ) \]

[Out]

Unintegrable(1/arctan(a*x),x)

Rubi [N/A]

Not integrable

Time = 0.00 (sec) , antiderivative size = 6, 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 = {} \[ \int \frac {1}{\arctan (a x)} \, dx=\int \frac {1}{\arctan (a x)} \, dx \]

[In]

Int[ArcTan[a*x]^(-1),x]

[Out]

Defer[Int][ArcTan[a*x]^(-1), x]

Rubi steps \begin{align*} \text {integral}& = \int \frac {1}{\arctan (a x)} \, dx \\ \end{align*}

Mathematica [N/A]

Not integrable

Time = 0.02 (sec) , antiderivative size = 8, normalized size of antiderivative = 1.33 \[ \int \frac {1}{\arctan (a x)} \, dx=\int \frac {1}{\arctan (a x)} \, dx \]

[In]

Integrate[ArcTan[a*x]^(-1),x]

[Out]

Integrate[ArcTan[a*x]^(-1), x]

Maple [N/A] (verified)

Not integrable

Time = 4.12 (sec) , antiderivative size = 6, normalized size of antiderivative = 1.00

\[\int \frac {1}{\arctan \left (a x \right )}d x\]

[In]

int(1/arctan(a*x),x)

[Out]

int(1/arctan(a*x),x)

Fricas [N/A]

Not integrable

Time = 0.25 (sec) , antiderivative size = 8, normalized size of antiderivative = 1.33 \[ \int \frac {1}{\arctan (a x)} \, dx=\int { \frac {1}{\arctan \left (a x\right )} \,d x } \]

[In]

integrate(1/arctan(a*x),x, algorithm="fricas")

[Out]

integral(1/arctan(a*x), x)

Sympy [N/A]

Not integrable

Time = 0.26 (sec) , antiderivative size = 7, normalized size of antiderivative = 1.17 \[ \int \frac {1}{\arctan (a x)} \, dx=\int \frac {1}{\operatorname {atan}{\left (a x \right )}}\, dx \]

[In]

integrate(1/atan(a*x),x)

[Out]

Integral(1/atan(a*x), x)

Maxima [N/A]

Not integrable

Time = 0.23 (sec) , antiderivative size = 8, normalized size of antiderivative = 1.33 \[ \int \frac {1}{\arctan (a x)} \, dx=\int { \frac {1}{\arctan \left (a x\right )} \,d x } \]

[In]

integrate(1/arctan(a*x),x, algorithm="maxima")

[Out]

integrate(1/arctan(a*x), x)

Giac [N/A]

Not integrable

Time = 21.74 (sec) , antiderivative size = 3, normalized size of antiderivative = 0.50 \[ \int \frac {1}{\arctan (a x)} \, dx=\int { \frac {1}{\arctan \left (a x\right )} \,d x } \]

[In]

integrate(1/arctan(a*x),x, algorithm="giac")

[Out]

sage0*x

Mupad [N/A]

Not integrable

Time = 0.29 (sec) , antiderivative size = 8, normalized size of antiderivative = 1.33 \[ \int \frac {1}{\arctan (a x)} \, dx=\int \frac {1}{\mathrm {atan}\left (a\,x\right )} \,d x \]

[In]

int(1/atan(a*x),x)

[Out]

int(1/atan(a*x), x)