Optimal. Leaf size=13 \[ \frac {x \log (x)}{\sqrt {b x^2}} \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.00, antiderivative size = 13, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 2, integrand size = 9, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.222, Rules used = {15, 29}
\begin {gather*} \frac {x \log (x)}{\sqrt {b x^2}} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 15
Rule 29
Rubi steps
\begin {align*} \int \frac {1}{\sqrt {b x^2}} \, dx &=\frac {x \int \frac {1}{x} \, dx}{\sqrt {b x^2}}\\ &=\frac {x \log (x)}{\sqrt {b x^2}}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A]
time = 0.00, size = 13, normalized size = 1.00 \begin {gather*} \frac {x \log (x)}{\sqrt {b x^2}} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.02, size = 12, normalized size = 0.92
method | result | size |
default | \(\frac {x \ln \left (x \right )}{\sqrt {b \,x^{2}}}\) | \(12\) |
risch | \(\frac {x \ln \left (x \right )}{\sqrt {b \,x^{2}}}\) | \(12\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.28, size = 6, normalized size = 0.46 \begin {gather*} \frac {\log \left (x\right )}{\sqrt {b}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.35, size = 16, normalized size = 1.23 \begin {gather*} \frac {\sqrt {b x^{2}} \log \left (x\right )}{b x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {1}{\sqrt {b x^{2}}}\, dx \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 1.01, size = 19, normalized size = 1.46 \begin {gather*} \frac {\log \left (\sqrt {{\left | b \right |}} {\left | x \right |} {\left | \mathrm {sgn}\left (x\right ) \right |}\right )}{\sqrt {b} \mathrm {sgn}\left (x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 1.09, size = 10, normalized size = 0.77 \begin {gather*} \frac {\ln \left (b\,x\right )\,\mathrm {sign}\left (x\right )}{\sqrt {b}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________