3.1.75 \(\int (c+d x)^m \csc (a+b x) \, dx\) [75]

Optimal. Leaf size=17 \[ \text {Int}\left ((c+d x)^m \csc (a+b x),x\right ) \]

[Out]

Unintegrable((d*x+c)^m*csc(b*x+a),x)

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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 (c+d x)^m \csc (a+b x) \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(c + d*x)^m*Csc[a + b*x],x]

[Out]

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

Rubi steps

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

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Mathematica [A]
time = 5.38, size = 0, normalized size = 0.00 \begin {gather*} \int (c+d x)^m \csc (a+b x) \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Integrate[(c + d*x)^m*Csc[a + b*x],x]

[Out]

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

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Maple [A]
time = 0.02, size = 0, normalized size = 0.00 \[\int \left (d x +c \right )^{m} \csc \left (b x +a \right )\, dx\]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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

[Out]

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

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

[Out]

integral((d*x + c)^m*csc(b*x + a), x)

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Sympy [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \left (c + d x\right )^{m} \csc {\left (a + b x \right )}\, dx \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

Integral((c + d*x)**m*csc(a + b*x), x)

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

[Out]

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

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Mupad [A]
time = 0.00, size = -1, normalized size = -0.06 \begin {gather*} \int \frac {{\left (c+d\,x\right )}^m}{\sin \left (a+b\,x\right )} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((c + d*x)^m/sin(a + b*x),x)

[Out]

int((c + d*x)^m/sin(a + b*x), x)

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