Optimal. Leaf size=24 \[ 8 \text {Int}\left (\frac {\csc ^3(2 a+2 b x)}{c+d x},x\right ) \]
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Rubi [A] time = 0.09, 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 = {} \[ \int \frac {\csc ^3(a+b x) \sec ^3(a+b x)}{c+d x} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin {align*} \int \frac {\csc ^3(a+b x) \sec ^3(a+b x)}{c+d x} \, dx &=8 \int \frac {\csc ^3(2 a+2 b x)}{c+d x} \, dx\\ \end {align*}
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Mathematica [A] time = 28.70, size = 0, normalized size = 0.00 \[ \int \frac {\csc ^3(a+b x) \sec ^3(a+b x)}{c+d x} \, dx \]
Verification is Not applicable to the result.
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fricas [A] time = 0.51, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {\csc \left (b x + a\right )^{3} \sec \left (b x + a\right )^{3}}{d x + c}, x\right ) \]
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 \[ \int \frac {\csc \left (b x + a\right )^{3} \sec \left (b x + a\right )^{3}}{d x + c}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 1.05, size = 0, normalized size = 0.00 \[ \int \frac {\left (\csc ^{3}\left (b x +a \right )\right ) \left (\sec ^{3}\left (b x +a \right )\right )}{d x +c}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [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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mupad [A] time = 0.00, size = -1, normalized size = -0.04 \[ \int \frac {1}{{\cos \left (a+b\,x\right )}^3\,{\sin \left (a+b\,x\right )}^3\,\left (c+d\,x\right )} \,d x \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {\csc ^{3}{\left (a + b x \right )} \sec ^{3}{\left (a + b x \right )}}{c + d x}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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