Optimal. Leaf size=27 \[ \text {Int}\left (\csc ^2(a+b x) \sec ^3(a+b x) (c+d x)^m,x\right ) \]
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Rubi [A] time = 0.23, 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 = {} \[ \int (c+d x)^m \csc ^2(a+b x) \sec ^3(a+b x) \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin {align*} \int (c+d x)^m \csc ^2(a+b x) \sec ^3(a+b x) \, dx &=\int (c+d x)^m \csc ^2(a+b x) \sec ^3(a+b x) \, dx\\ \end {align*}
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Mathematica [A] time = 30.51, size = 0, normalized size = 0.00 \[ \int (c+d x)^m \csc ^2(a+b x) \sec ^3(a+b x) \, dx \]
Verification is Not applicable to the result.
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fricas [A] time = 0.46, size = 0, normalized size = 0.00 \[ {\rm integral}\left ({\left (d x + c\right )}^{m} \csc \left (b x + a\right )^{2} \sec \left (b x + a\right )^{3}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.00, size = 0, normalized size = 0.00 \[ \int {\left (d x + c\right )}^{m} \csc \left (b x + a\right )^{2} \sec \left (b x + a\right )^{3}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.14, size = 0, normalized size = 0.00 \[ \int \left (d x +c \right )^{m} \left (\csc ^{2}\left (b x +a \right )\right ) \left (\sec ^{3}\left (b x +a \right )\right )\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.00, size = 0, normalized size = 0.00 \[ \int {\left (d x + c\right )}^{m} \csc \left (b x + a\right )^{2} \sec \left (b x + a\right )^{3}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [A] time = 0.00, size = -1, normalized size = -0.04 \[ \int \frac {{\left (c+d\,x\right )}^m}{{\cos \left (a+b\,x\right )}^3\,{\sin \left (a+b\,x\right )}^2} \,d x \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [F(-1)] time = 0.00, size = 0, normalized size = 0.00 \[ \text {Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
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