Optimal. Leaf size=23 \[ \text {Int}\left (\frac {\left (a+b \text {sech}\left (c+d \sqrt {x}\right )\right )^2}{x^2},x\right ) \]
[Out]
________________________________________________________________________________________
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 {\left (a+b \text {sech}\left (c+d \sqrt {x}\right )\right )^2}{x^2} \, dx \end {gather*}
Verification is not applicable to the result.
[In]
[Out]
Rubi steps
\begin {align*} \int \frac {\left (a+b \text {sech}\left (c+d \sqrt {x}\right )\right )^2}{x^2} \, dx &=\int \frac {\left (a+b \text {sech}\left (c+d \sqrt {x}\right )\right )^2}{x^2} \, dx\\ \end {align*}
________________________________________________________________________________________
Mathematica [A]
time = 18.30, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {\left (a+b \text {sech}\left (c+d \sqrt {x}\right )\right )^2}{x^2} \, dx \end {gather*}
Verification is not applicable to the result.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 3.21, size = 0, normalized size = 0.00 \[\int \frac {\left (a +b \,\mathrm {sech}\left (c +d \sqrt {x}\right )\right )^{2}}{x^{2}}\, dx\]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
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.
[In]
[Out]
________________________________________________________________________________________
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.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {\left (a + b \operatorname {sech}{\left (c + d \sqrt {x} \right )}\right )^{2}}{x^{2}}\, dx \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
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.
[In]
[Out]
________________________________________________________________________________________
Mupad [A]
time = 0.00, size = -1, normalized size = -0.04 \begin {gather*} \int \frac {{\left (a+\frac {b}{\mathrm {cosh}\left (c+d\,\sqrt {x}\right )}\right )}^2}{x^2} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________