3.2.24 \(\int \frac {(b x)^m}{\text {ArcCos}(a x)^2} \, dx\) [124]

Optimal. Leaf size=15 \[ \text {Int}\left (\frac {(b x)^m}{\text {ArcCos}(a x)^2},x\right ) \]

[Out]

Unintegrable((b*x)^m/arccos(a*x)^2,x)

________________________________________________________________________________________

Rubi [A]
time = 0.01, 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 = {} \begin {gather*} \int \frac {(b x)^m}{\text {ArcCos}(a x)^2} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

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

[Out]

Defer[Int][(b*x)^m/ArcCos[a*x]^2, x]

Rubi steps

\begin {align*} \int \frac {(b x)^m}{\cos ^{-1}(a x)^2} \, dx &=\int \frac {(b x)^m}{\cos ^{-1}(a x)^2} \, dx\\ \end {align*}

________________________________________________________________________________________

Mathematica [A]
time = 0.59, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {(b x)^m}{\text {ArcCos}(a x)^2} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

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

[Out]

Integrate[(b*x)^m/ArcCos[a*x]^2, x]

________________________________________________________________________________________

Maple [A]
time = 1.08, size = 0, normalized size = 0.00 \[\int \frac {\left (b x \right )^{m}}{\arccos \left (a x \right )^{2}}\, dx\]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((b*x)^m/arccos(a*x)^2,x)

[Out]

int((b*x)^m/arccos(a*x)^2,x)

________________________________________________________________________________________

Maxima [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Failed to integrate} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

________________________________________________________________________________________

Fricas [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

integral((b*x)^m/arccos(a*x)^2, x)

________________________________________________________________________________________

Sympy [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {\left (b x\right )^{m}}{\operatorname {acos}^{2}{\left (a x \right )}}\, dx \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((b*x)**m/acos(a*x)**2,x)

[Out]

Integral((b*x)**m/acos(a*x)**2, x)

________________________________________________________________________________________

Giac [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

integrate((b*x)^m/arccos(a*x)^2, x)

________________________________________________________________________________________

Mupad [A]
time = 0.00, size = -1, normalized size = -0.07 \begin {gather*} \int \frac {{\left (b\,x\right )}^m}{{\mathrm {acos}\left (a\,x\right )}^2} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((b*x)^m/acos(a*x)^2,x)

[Out]

int((b*x)^m/acos(a*x)^2, x)

________________________________________________________________________________________