\(\int \frac {1}{x^2 \arccos (a x)^3} \, dx\) [66]

Optimal result

Integrand size = 10, antiderivative size = 10 \[ \int \frac {1}{x^2 \arccos (a x)^3} \, dx=\text {Int}\left (\frac {1}{x^2 \arccos (a x)^3},x\right ) \]

[Out]

Unintegrable(1/x^2/arccos(a*x)^3,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 = {} \[ \int \frac {1}{x^2 \arccos (a x)^3} \, dx=\int \frac {1}{x^2 \arccos (a x)^3} \, dx \]

[In]

Int[1/(x^2*ArcCos[a*x]^3),x]

[Out]

Defer[Int][1/(x^2*ArcCos[a*x]^3), x]

Rubi steps \begin{align*} \text {integral}& = \int \frac {1}{x^2 \arccos (a x)^3} \, dx \\ \end{align*}

Mathematica [N/A]

Not integrable

Time = 7.67 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.20 \[ \int \frac {1}{x^2 \arccos (a x)^3} \, dx=\int \frac {1}{x^2 \arccos (a x)^3} \, dx \]

[In]

Integrate[1/(x^2*ArcCos[a*x]^3),x]

[Out]

Integrate[1/(x^2*ArcCos[a*x]^3), x]

Maple [N/A] (verified)

Not integrable

Time = 1.67 (sec) , antiderivative size = 10, normalized size of antiderivative = 1.00

\[\int \frac {1}{x^{2} \arccos \left (a x \right )^{3}}d x\]

[In]

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

[Out]

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

Fricas [N/A]

Not integrable

Time = 0.24 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.20 \[ \int \frac {1}{x^2 \arccos (a x)^3} \, dx=\int { \frac {1}{x^{2} \arccos \left (a x\right )^{3}} \,d x } \]

[In]

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

[Out]

integral(1/(x^2*arccos(a*x)^3), x)

Sympy [N/A]

Not integrable

Time = 0.59 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.20 \[ \int \frac {1}{x^2 \arccos (a x)^3} \, dx=\int \frac {1}{x^{2} \operatorname {acos}^{3}{\left (a x \right )}}\, dx \]

[In]

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

[Out]

Integral(1/(x**2*acos(a*x)**3), x)

Maxima [N/A]

Not integrable

Time = 1.70 (sec) , antiderivative size = 143, normalized size of antiderivative = 14.30 \[ \int \frac {1}{x^2 \arccos (a x)^3} \, dx=\int { \frac {1}{x^{2} \arccos \left (a x\right )^{3}} \,d x } \]

[In]

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

[Out]

-1/2*(x^3*arctan2(sqrt(a*x + 1)*sqrt(-a*x + 1), a*x)^2*integrate((a^2*x^2 - 6)/(x^4*arctan2(sqrt(a*x + 1)*sqrt
(-a*x + 1), a*x)), x) - sqrt(a*x + 1)*sqrt(-a*x + 1)*a*x + (a^2*x^2 - 2)*arctan2(sqrt(a*x + 1)*sqrt(-a*x + 1),
a*x))/(a^2*x^3*arctan2(sqrt(a*x + 1)*sqrt(-a*x + 1), a*x)^2)

Giac [N/A]

Not integrable

Time = 0.39 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.20 \[ \int \frac {1}{x^2 \arccos (a x)^3} \, dx=\int { \frac {1}{x^{2} \arccos \left (a x\right )^{3}} \,d x } \]

[In]

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

[Out]

integrate(1/(x^2*arccos(a*x)^3), x)

Mupad [N/A]

Not integrable

Time = 0.24 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.20 \[ \int \frac {1}{x^2 \arccos (a x)^3} \, dx=\int \frac {1}{x^2\,{\mathrm {acos}\left (a\,x\right )}^3} \,d x \]

[In]

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

[Out]

int(1/(x^2*acos(a*x)^3), x)