\(\int \frac {1}{x^2 \arccos (a x)^2} \, dx\) [59]

Optimal result

Integrand size = 10, antiderivative size = 10 \[ \int \frac {1}{x^2 \arccos (a x)^2} \, dx=\text {Int}\left (\frac {1}{x^2 \arccos (a x)^2},x\right ) \]

[Out]

Unintegrable(1/x^2/arccos(a*x)^2,x)

Rubi [N/A]

Not integrable

Time = 0.01 (sec) , antiderivative size = 10, 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 = {} \[ \int \frac {1}{x^2 \arccos (a x)^2} \, dx=\int \frac {1}{x^2 \arccos (a x)^2} \, dx \]

[In]

Int[1/(x^2*ArcCos[a*x]^2),x]

[Out]

Defer[Int][1/(x^2*ArcCos[a*x]^2), x]

Rubi steps \begin{align*} \text {integral}& = \int \frac {1}{x^2 \arccos (a x)^2} \, dx \\ \end{align*}

Mathematica [N/A]

Not integrable

Time = 14.83 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.20 \[ \int \frac {1}{x^2 \arccos (a x)^2} \, dx=\int \frac {1}{x^2 \arccos (a x)^2} \, dx \]

[In]

Integrate[1/(x^2*ArcCos[a*x]^2),x]

[Out]

Integrate[1/(x^2*ArcCos[a*x]^2), x]

Maple [N/A] (verified)

Not integrable

Time = 1.76 (sec) , antiderivative size = 10, normalized size of antiderivative = 1.00

\[\int \frac {1}{x^{2} \arccos \left (a x \right )^{2}}d x\]

[In]

int(1/x^2/arccos(a*x)^2,x)

[Out]

int(1/x^2/arccos(a*x)^2,x)

Fricas [N/A]

Not integrable

Time = 0.24 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.20 \[ \int \frac {1}{x^2 \arccos (a x)^2} \, dx=\int { \frac {1}{x^{2} \arccos \left (a x\right )^{2}} \,d x } \]

[In]

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

[Out]

integral(1/(x^2*arccos(a*x)^2), x)

Sympy [N/A]

Not integrable

Time = 0.44 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.20 \[ \int \frac {1}{x^2 \arccos (a x)^2} \, dx=\int \frac {1}{x^{2} \operatorname {acos}^{2}{\left (a x \right )}}\, dx \]

[In]

integrate(1/x**2/acos(a*x)**2,x)

[Out]

Integral(1/(x**2*acos(a*x)**2), x)

Maxima [N/A]

Not integrable

Time = 0.65 (sec) , antiderivative size = 136, normalized size of antiderivative = 13.60 \[ \int \frac {1}{x^2 \arccos (a x)^2} \, dx=\int { \frac {1}{x^{2} \arccos \left (a x\right )^{2}} \,d x } \]

[In]

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

[Out]

(a*x^2*arctan2(sqrt(a*x + 1)*sqrt(-a*x + 1), a*x)*integrate((a^2*x^2 - 2)*sqrt(a*x + 1)*sqrt(-a*x + 1)/((a^3*x
^5 - a*x^3)*arctan2(sqrt(a*x + 1)*sqrt(-a*x + 1), a*x)), x) + sqrt(a*x + 1)*sqrt(-a*x + 1))/(a*x^2*arctan2(sqr
t(a*x + 1)*sqrt(-a*x + 1), a*x))

Giac [N/A]

Not integrable

Time = 0.36 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.20 \[ \int \frac {1}{x^2 \arccos (a x)^2} \, dx=\int { \frac {1}{x^{2} \arccos \left (a x\right )^{2}} \,d x } \]

[In]

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

[Out]

integrate(1/(x^2*arccos(a*x)^2), x)

Mupad [N/A]

Not integrable

Time = 0.25 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.20 \[ \int \frac {1}{x^2 \arccos (a x)^2} \, dx=\int \frac {1}{x^2\,{\mathrm {acos}\left (a\,x\right )}^2} \,d x \]

[In]

int(1/(x^2*acos(a*x)^2),x)

[Out]

int(1/(x^2*acos(a*x)^2), x)