Optimal. Leaf size=19 \[ \text {Int}\left (\frac {\tanh ^3(e+f x)}{(c+d x)^2},x\right ) \]
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Rubi [A] time = 0.04, 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 = {} \[ \int \frac {\tanh ^3(e+f x)}{(c+d x)^2} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin {align*} \int \frac {\tanh ^3(e+f x)}{(c+d x)^2} \, dx &=\int \frac {\tanh ^3(e+f x)}{(c+d x)^2} \, dx\\ \end {align*}
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Mathematica [A] time = 23.15, size = 0, normalized size = 0.00 \[ \int \frac {\tanh ^3(e+f x)}{(c+d x)^2} \, dx \]
Verification is Not applicable to the result.
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fricas [A] time = 0.51, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {\tanh \left (f x + e\right )^{3}}{d^{2} x^{2} + 2 \, c d x + c^{2}}, x\right ) \]
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 \[ \int \frac {\tanh \left (f x + e\right )^{3}}{{\left (d x + c\right )}^{2}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.98, size = 0, normalized size = 0.00 \[ \int \frac {\tanh ^{3}\left (f x +e \right )}{\left (d x +c \right )^{2}}\, dx \]
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 \[ -\frac {d^{2} f^{2} x^{2} + 2 \, c d f^{2} x + c^{2} f^{2} + 2 \, d^{2} + {\left (d^{2} f^{2} x^{2} e^{\left (4 \, e\right )} + 2 \, c d f^{2} x e^{\left (4 \, e\right )} + c^{2} f^{2} e^{\left (4 \, e\right )}\right )} e^{\left (4 \, f x\right )} + 2 \, {\left (d^{2} f^{2} x^{2} e^{\left (2 \, e\right )} + c^{2} f^{2} e^{\left (2 \, e\right )} - c d f e^{\left (2 \, e\right )} + d^{2} e^{\left (2 \, e\right )} + {\left (2 \, c d f^{2} e^{\left (2 \, e\right )} - d^{2} f e^{\left (2 \, e\right )}\right )} x\right )} e^{\left (2 \, f x\right )}}{d^{4} f^{2} x^{3} + 3 \, c d^{3} f^{2} x^{2} + 3 \, c^{2} d^{2} f^{2} x + c^{3} d f^{2} + {\left (d^{4} f^{2} x^{3} e^{\left (4 \, e\right )} + 3 \, c d^{3} f^{2} x^{2} e^{\left (4 \, e\right )} + 3 \, c^{2} d^{2} f^{2} x e^{\left (4 \, e\right )} + c^{3} d f^{2} e^{\left (4 \, e\right )}\right )} e^{\left (4 \, f x\right )} + 2 \, {\left (d^{4} f^{2} x^{3} e^{\left (2 \, e\right )} + 3 \, c d^{3} f^{2} x^{2} e^{\left (2 \, e\right )} + 3 \, c^{2} d^{2} f^{2} x e^{\left (2 \, e\right )} + c^{3} d f^{2} e^{\left (2 \, e\right )}\right )} e^{\left (2 \, f x\right )}} - \int \frac {2 \, {\left (d^{2} f^{2} x^{2} + 2 \, c d f^{2} x + c^{2} f^{2} + 3 \, d^{2}\right )}}{d^{4} f^{2} x^{4} + 4 \, c d^{3} f^{2} x^{3} + 6 \, c^{2} d^{2} f^{2} x^{2} + 4 \, c^{3} d f^{2} x + c^{4} f^{2} + {\left (d^{4} f^{2} x^{4} e^{\left (2 \, e\right )} + 4 \, c d^{3} f^{2} x^{3} e^{\left (2 \, e\right )} + 6 \, c^{2} d^{2} f^{2} x^{2} e^{\left (2 \, e\right )} + 4 \, c^{3} d f^{2} x e^{\left (2 \, e\right )} + c^{4} f^{2} e^{\left (2 \, e\right )}\right )} e^{\left (2 \, f x\right )}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [A] time = 0.00, size = -1, normalized size = -0.05 \[ \int \frac {{\mathrm {tanh}\left (e+f\,x\right )}^3}{{\left (c+d\,x\right )}^2} \,d x \]
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 \[ \int \frac {\tanh ^{3}{\left (e + f x \right )}}{\left (c + d x\right )^{2}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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