Optimal. Leaf size=19 \[ \text {Int}\left (\frac {\text {sech}^3(a+b x)}{c+d x},x\right ) \]
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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 = {} \[ \int \frac {\text {sech}^3(a+b x)}{c+d x} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin {align*} \int \frac {\text {sech}^3(a+b x)}{c+d x} \, dx &=\int \frac {\text {sech}^3(a+b x)}{c+d x} \, dx\\ \end {align*}
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Mathematica [F] time = 180.01, size = 0, normalized size = 0.00 \[ \text {\$Aborted} \]
Verification is Not applicable to the result.
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fricas [A] time = 0.86, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {\operatorname {sech}\left (b x + a\right )^{3}}{d x + c}, x\right ) \]
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 \[ \int \frac {\operatorname {sech}\left (b x + a\right )^{3}}{d x + c}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.52, size = 0, normalized size = 0.00 \[ \int \frac {\mathrm {sech}\left (b x +a \right )^{3}}{d x +c}\, dx \]
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 \[ \frac {{\left (b d x e^{\left (3 \, a\right )} + {\left (b c - d\right )} e^{\left (3 \, a\right )}\right )} e^{\left (3 \, b x\right )} - {\left (b d x e^{a} + {\left (b c + d\right )} e^{a}\right )} e^{\left (b x\right )}}{b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2} + {\left (b^{2} d^{2} x^{2} e^{\left (4 \, a\right )} + 2 \, b^{2} c d x e^{\left (4 \, a\right )} + b^{2} c^{2} e^{\left (4 \, a\right )}\right )} e^{\left (4 \, b x\right )} + 2 \, {\left (b^{2} d^{2} x^{2} e^{\left (2 \, a\right )} + 2 \, b^{2} c d x e^{\left (2 \, a\right )} + b^{2} c^{2} e^{\left (2 \, a\right )}\right )} e^{\left (2 \, b x\right )}} + 8 \, \int \frac {{\left (b^{2} d^{2} x^{2} e^{a} + 2 \, b^{2} c d x e^{a} + {\left (b^{2} c^{2} - 2 \, d^{2}\right )} e^{a}\right )} e^{\left (b x\right )}}{8 \, {\left (b^{2} d^{3} x^{3} + 3 \, b^{2} c d^{2} x^{2} + 3 \, b^{2} c^{2} d x + b^{2} c^{3} + {\left (b^{2} d^{3} x^{3} e^{\left (2 \, a\right )} + 3 \, b^{2} c d^{2} x^{2} e^{\left (2 \, a\right )} + 3 \, b^{2} c^{2} d x e^{\left (2 \, a\right )} + b^{2} c^{3} e^{\left (2 \, a\right )}\right )} e^{\left (2 \, b x\right )}\right )}}\,{d x} \]
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 \[ \int \frac {1}{{\mathrm {cosh}\left (a+b\,x\right )}^3\,\left (c+d\,x\right )} \,d x \]
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 \[ \int \frac {\operatorname {sech}^{3}{\left (a + b x \right )}}{c + d x}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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