3.177 \(\int (c+d x)^m \cot ^3(a+b x) \, dx\)

Optimal. Leaf size=18 \[ \text{Unintegrable}\left (\cot ^3(a+b x) (c+d x)^m,x\right ) \]

[Out]

Unintegrable[(c + d*x)^m*Cot[a + b*x]^3, x]

________________________________________________________________________________________

Rubi [A]  time = 0.0356774, antiderivative size = 0, normalized size of antiderivative = 0., number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0., Rules used = {} \[ \int (c+d x)^m \cot ^3(a+b x) \, dx \]

Verification is Not applicable to the result.

[In]

Int[(c + d*x)^m*Cot[a + b*x]^3,x]

[Out]

Defer[Int][(c + d*x)^m*Cot[a + b*x]^3, x]

Rubi steps

\begin{align*} \int (c+d x)^m \cot ^3(a+b x) \, dx &=\int (c+d x)^m \cot ^3(a+b x) \, dx\\ \end{align*}

Mathematica [A]  time = 5.53587, size = 0, normalized size = 0. \[ \int (c+d x)^m \cot ^3(a+b x) \, dx \]

Verification is Not applicable to the result.

[In]

Integrate[(c + d*x)^m*Cot[a + b*x]^3,x]

[Out]

Integrate[(c + d*x)^m*Cot[a + b*x]^3, x]

________________________________________________________________________________________

Maple [A]  time = 0.178, size = 0, normalized size = 0. \begin{align*} \int \left ( dx+c \right ) ^{m} \left ( \cot \left ( bx+a \right ) \right ) ^{3}\, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((d*x+c)^m*cot(b*x+a)^3,x)

[Out]

int((d*x+c)^m*cot(b*x+a)^3,x)

________________________________________________________________________________________

Maxima [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int{\left (d x + c\right )}^{m} \cot \left (b x + a\right )^{3}\,{d x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((d*x+c)^m*cot(b*x+a)^3,x, algorithm="maxima")

[Out]

integrate((d*x + c)^m*cot(b*x + a)^3, x)

________________________________________________________________________________________

Fricas [A]  time = 0., size = 0, normalized size = 0. \begin{align*}{\rm integral}\left ({\left (d x + c\right )}^{m} \cot \left (b x + a\right )^{3}, x\right ) \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((d*x+c)^m*cot(b*x+a)^3,x, algorithm="fricas")

[Out]

integral((d*x + c)^m*cot(b*x + a)^3, x)

________________________________________________________________________________________

Sympy [F(-1)]  time = 0., size = 0, normalized size = 0. \begin{align*} \text{Timed out} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((d*x+c)**m*cot(b*x+a)**3,x)

[Out]

Timed out

________________________________________________________________________________________

Giac [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int{\left (d x + c\right )}^{m} \cot \left (b x + a\right )^{3}\,{d x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((d*x+c)^m*cot(b*x+a)^3,x, algorithm="giac")

[Out]

integrate((d*x + c)^m*cot(b*x + a)^3, x)