Optimal. Leaf size=26 \[ \text {Int}\left (\frac {\tan ^m(c+d x)}{a+b \sin ^n(c+d x)},x\right ) \]
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Rubi [A] time = 0.06, 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 = {} \[ \int \frac {\tan ^m(c+d x)}{a+b \sin ^n(c+d x)} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin {align*} \int \frac {\tan ^m(c+d x)}{a+b \sin ^n(c+d x)} \, dx &=\int \frac {\tan ^m(c+d x)}{a+b \sin ^n(c+d x)} \, dx\\ \end {align*}
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Mathematica [A] time = 2.45, size = 0, normalized size = 0.00 \[ \int \frac {\tan ^m(c+d x)}{a+b \sin ^n(c+d x)} \, dx \]
Verification is Not applicable to the result.
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fricas [A] time = 0.46, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {\tan \left (d x + c\right )^{m}}{b \sin \left (d x + c\right )^{n} + a}, x\right ) \]
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 \[ \int \frac {\tan \left (d x + c\right )^{m}}{b \sin \left (d x + c\right )^{n} + a}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 1.57, size = 0, normalized size = 0.00 \[ \int \frac {\tan ^{m}\left (d x +c \right )}{a +b \left (\sin ^{n}\left (d x +c \right )\right )}\, dx \]
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 \[ \int \frac {\tan \left (d x + c\right )^{m}}{b \sin \left (d x + c\right )^{n} + a}\,{d x} \]
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 \[ \int \frac {{\mathrm {tan}\left (c+d\,x\right )}^m}{a+b\,{\sin \left (c+d\,x\right )}^n} \,d x \]
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 \[ \int \frac {\tan ^{m}{\left (c + d x \right )}}{a + b \sin ^{n}{\left (c + d x \right )}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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