Optimal. Leaf size=23 \[ \text {Int}\left (\frac {(a+b \tanh (e+f x))^3}{c+d x},x\right ) \]
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Rubi [A] time = 0.05, 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 = {} \[ \int \frac {(a+b \tanh (e+f x))^3}{c+d x} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin {align*} \int \frac {(a+b \tanh (e+f x))^3}{c+d x} \, dx &=\int \frac {(a+b \tanh (e+f x))^3}{c+d x} \, dx\\ \end {align*}
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Mathematica [A] time = 63.49, size = 0, normalized size = 0.00 \[ \int \frac {(a+b \tanh (e+f x))^3}{c+d x} \, dx \]
Verification is Not applicable to the result.
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fricas [A] time = 0.51, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {b^{3} \tanh \left (f x + e\right )^{3} + 3 \, a b^{2} \tanh \left (f x + e\right )^{2} + 3 \, a^{2} b \tanh \left (f x + e\right ) + a^{3}}{d x + c}, x\right ) \]
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 \[ \int \frac {{\left (b \tanh \left (f x + e\right ) + a\right )}^{3}}{d x + c}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 1.09, size = 0, normalized size = 0.00 \[ \int \frac {\left (a +b \tanh \left (f x +e \right )\right )^{3}}{d x +c}\, dx \]
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 \[ \frac {a^{3} \log \left (d x + c\right )}{d} + \frac {{\left (3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right )} \log \left (d x + c\right )}{d} + \frac {6 \, a b^{2} d f x + 6 \, a b^{2} c f - b^{3} d + {\left (6 \, a b^{2} c f e^{\left (2 \, e\right )} + {\left (2 \, c f e^{\left (2 \, e\right )} - d e^{\left (2 \, e\right )}\right )} b^{3} + 2 \, {\left (3 \, a b^{2} d f e^{\left (2 \, e\right )} + b^{3} d f e^{\left (2 \, e\right )}\right )} x\right )} e^{\left (2 \, f x\right )}}{d^{2} f^{2} x^{2} + 2 \, c d f^{2} x + c^{2} f^{2} + {\left (d^{2} f^{2} x^{2} e^{\left (4 \, e\right )} + 2 \, c d f^{2} x e^{\left (4 \, e\right )} + c^{2} f^{2} e^{\left (4 \, e\right )}\right )} e^{\left (4 \, f x\right )} + 2 \, {\left (d^{2} f^{2} x^{2} e^{\left (2 \, e\right )} + 2 \, c d f^{2} x e^{\left (2 \, e\right )} + c^{2} f^{2} e^{\left (2 \, e\right )}\right )} e^{\left (2 \, f x\right )}} - \int \frac {2 \, {\left (3 \, a^{2} b c^{2} f^{2} - 3 \, a b^{2} c d f + {\left (c^{2} f^{2} + d^{2}\right )} b^{3} + {\left (3 \, a^{2} b d^{2} f^{2} + b^{3} d^{2} f^{2}\right )} x^{2} + {\left (6 \, a^{2} b c d f^{2} + 2 \, b^{3} c d f^{2} - 3 \, a b^{2} d^{2} f\right )} x\right )}}{d^{3} f^{2} x^{3} + 3 \, c d^{2} f^{2} x^{2} + 3 \, c^{2} d f^{2} x + c^{3} f^{2} + {\left (d^{3} f^{2} x^{3} e^{\left (2 \, e\right )} + 3 \, c d^{2} f^{2} x^{2} e^{\left (2 \, e\right )} + 3 \, c^{2} d f^{2} x e^{\left (2 \, e\right )} + c^{3} f^{2} e^{\left (2 \, e\right )}\right )} e^{\left (2 \, f x\right )}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [A] time = 0.00, size = -1, normalized size = -0.04 \[ \int \frac {{\left (a+b\,\mathrm {tanh}\left (e+f\,x\right )\right )}^3}{c+d\,x} \,d x \]
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 \[ \int \frac {\left (a + b \tanh {\left (e + f x \right )}\right )^{3}}{c + d x}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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