Optimal. Leaf size=25 \[ \text {Int}\left (\frac {1}{x^{3/2} \left (a+b \text {sech}\left (c+d \sqrt {x}\right )\right )^2},x\right ) \]
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Rubi [A]
time = 0.02, 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 {1}{x^{3/2} \left (a+b \text {sech}\left (c+d \sqrt {x}\right )\right )^2} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {align*} \int \frac {1}{x^{3/2} \left (a+b \text {sech}\left (c+d \sqrt {x}\right )\right )^2} \, dx &=\int \frac {1}{x^{3/2} \left (a+b \text {sech}\left (c+d \sqrt {x}\right )\right )^2} \, dx\\ \end {align*}
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Mathematica [A]
time = 43.43, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {1}{x^{3/2} \left (a+b \text {sech}\left (c+d \sqrt {x}\right )\right )^2} \, dx \end {gather*}
Verification is not applicable to the result.
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Maple [A]
time = 3.48, size = 0, normalized size = 0.00 \[\int \frac {1}{x^{\frac {3}{2}} \left (a +b \,\mathrm {sech}\left (c +d \sqrt {x}\right )\right )^{2}}\, dx\]
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 \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 {1}{x^{\frac {3}{2}} \left (a + b \operatorname {sech}{\left (c + d \sqrt {x} \right )}\right )^{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 = -0.04 \begin {gather*} \int \frac {1}{x^{3/2}\,{\left (a+\frac {b}{\mathrm {cosh}\left (c+d\,\sqrt {x}\right )}\right )}^2} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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