Integrand size = 16, antiderivative size = 16 \[ \int \sqrt {c+d x} \text {sech}(a+b x) \, dx=\text {Int}\left (\sqrt {c+d x} \text {sech}(a+b x),x\right ) \]
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Not integrable
Time = 0.02 (sec) , antiderivative size = 16, normalized size of antiderivative = 1.00, number of steps used = 0, number of rules used = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \[ \int \sqrt {c+d x} \text {sech}(a+b x) \, dx=\int \sqrt {c+d x} \text {sech}(a+b x) \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \sqrt {c+d x} \text {sech}(a+b x) \, dx \\ \end{align*}
Not integrable
Time = 3.43 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.12 \[ \int \sqrt {c+d x} \text {sech}(a+b x) \, dx=\int \sqrt {c+d x} \text {sech}(a+b x) \, dx \]
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Not integrable
Time = 0.04 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.88
\[\int \operatorname {sech}\left (b x +a \right ) \sqrt {d x +c}d x\]
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Not integrable
Time = 0.27 (sec) , antiderivative size = 16, normalized size of antiderivative = 1.00 \[ \int \sqrt {c+d x} \text {sech}(a+b x) \, dx=\int { \sqrt {d x + c} \operatorname {sech}\left (b x + a\right ) \,d x } \]
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Not integrable
Time = 1.28 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.94 \[ \int \sqrt {c+d x} \text {sech}(a+b x) \, dx=\int \sqrt {c + d x} \operatorname {sech}{\left (a + b x \right )}\, dx \]
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Not integrable
Time = 0.78 (sec) , antiderivative size = 16, normalized size of antiderivative = 1.00 \[ \int \sqrt {c+d x} \text {sech}(a+b x) \, dx=\int { \sqrt {d x + c} \operatorname {sech}\left (b x + a\right ) \,d x } \]
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Not integrable
Time = 0.30 (sec) , antiderivative size = 16, normalized size of antiderivative = 1.00 \[ \int \sqrt {c+d x} \text {sech}(a+b x) \, dx=\int { \sqrt {d x + c} \operatorname {sech}\left (b x + a\right ) \,d x } \]
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Not integrable
Time = 1.74 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.12 \[ \int \sqrt {c+d x} \text {sech}(a+b x) \, dx=\int \frac {\sqrt {c+d\,x}}{\mathrm {cosh}\left (a+b\,x\right )} \,d x \]
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