Optimal. Leaf size=30 \[ -\frac {2 a}{\sqrt {x}}+b \text {Int}\left (\frac {\text {sech}\left (c+d \sqrt {x}\right )}{x^{3/2}},x\right ) \]
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Rubi [A]
time = 0.01, 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 = {}
\begin {gather*} \int \frac {a+b \text {sech}\left (c+d \sqrt {x}\right )}{x^{3/2}} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {align*} \int \frac {a+b \text {sech}\left (c+d \sqrt {x}\right )}{x^{3/2}} \, dx &=\int \left (\frac {a}{x^{3/2}}+\frac {b \text {sech}\left (c+d \sqrt {x}\right )}{x^{3/2}}\right ) \, dx\\ &=-\frac {2 a}{\sqrt {x}}+b \int \frac {\text {sech}\left (c+d \sqrt {x}\right )}{x^{3/2}} \, dx\\ \end {align*}
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Mathematica [A]
time = 6.32, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {a+b \text {sech}\left (c+d \sqrt {x}\right )}{x^{3/2}} \, dx \end {gather*}
Verification is not applicable to the result.
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Maple [A]
time = 2.88, size = 0, normalized size = 0.00 \[\int \frac {a +b \,\mathrm {sech}\left (c +d \sqrt {x}\right )}{x^{\frac {3}{2}}}\, dx\]
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 \begin {gather*} \text {Failed to integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}
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 \begin {gather*} \int \frac {a + b \operatorname {sech}{\left (c + d \sqrt {x} \right )}}{x^{\frac {3}{2}}}\, dx \end {gather*}
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 \begin {gather*} \text {could not integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [A]
time = 0.00, size = -1, normalized size = -0.03 \begin {gather*} \int \frac {a+\frac {b}{\mathrm {cosh}\left (c+d\,\sqrt {x}\right )}}{x^{3/2}} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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