3.51 \(\int \frac {1}{\tan ^{-1}(a x)^{3/2}} \, dx\)

Optimal. Leaf size=11 \[ \text {Int}\left (\frac {1}{\tan ^{-1}(a x)^{3/2}},x\right ) \]

[Out]

Unintegrable(1/arctan(a*x)^(3/2),x)

________________________________________________________________________________________

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 = {} \[ \int \frac {1}{\tan ^{-1}(a x)^{3/2}} \, dx \]

Verification is Not applicable to the result.

[In]

Int[ArcTan[a*x]^(-3/2),x]

[Out]

Defer[Int][ArcTan[a*x]^(-3/2), x]

Rubi steps

\begin {align*} \int \frac {1}{\tan ^{-1}(a x)^{3/2}} \, dx &=\int \frac {1}{\tan ^{-1}(a x)^{3/2}} \, dx\\ \end {align*}

________________________________________________________________________________________

Mathematica [A]  time = 2.72, size = 0, normalized size = 0.00 \[ \int \frac {1}{\tan ^{-1}(a x)^{3/2}} \, dx \]

Verification is Not applicable to the result.

[In]

Integrate[ArcTan[a*x]^(-3/2),x]

[Out]

Integrate[ArcTan[a*x]^(-3/2), x]

________________________________________________________________________________________

fricas [F(-2)]  time = 0.00, size = 0, normalized size = 0.00 \[ \text {Exception raised: TypeError} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/arctan(a*x)^(3/2),x, algorithm="fricas")

[Out]

Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (co
nstant residues)

________________________________________________________________________________________

giac [F(-1)]  time = 0.00, size = 0, normalized size = 0.00 \[ \text {Timed out} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/arctan(a*x)^(3/2),x, algorithm="giac")

[Out]

Timed out

________________________________________________________________________________________

maple [A]  time = 0.51, size = 0, normalized size = 0.00 \[ \int \frac {1}{\arctan \left (a x \right )^{\frac {3}{2}}}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/arctan(a*x)^(3/2),x)

[Out]

int(1/arctan(a*x)^(3/2),x)

________________________________________________________________________________________

maxima [F(-2)]  time = 0.00, size = 0, normalized size = 0.00 \[ \text {Exception raised: RuntimeError} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/arctan(a*x)^(3/2),x, algorithm="maxima")

[Out]

Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative e
xponent.

________________________________________________________________________________________

mupad [A]  time = 0.00, size = -1, normalized size = -0.09 \[ \int \frac {1}{{\mathrm {atan}\left (a\,x\right )}^{3/2}} \,d x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/atan(a*x)^(3/2),x)

[Out]

int(1/atan(a*x)^(3/2), x)

________________________________________________________________________________________

sympy [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {1}{\operatorname {atan}^{\frac {3}{2}}{\left (a x \right )}}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/atan(a*x)**(3/2),x)

[Out]

Integral(atan(a*x)**(-3/2), x)

________________________________________________________________________________________