Optimal. Leaf size=17 \[ x-\frac {1}{x}-\frac {10}{3} \tan ^{-1}\left (\frac {x}{3}\right ) \]
________________________________________________________________________________________
Rubi [A] time = 0.01, antiderivative size = 17, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 2, integrand size = 16, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.125, Rules used = {1262, 203} \begin {gather*} x-\frac {1}{x}-\frac {10}{3} \tan ^{-1}\left (\frac {x}{3}\right ) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 203
Rule 1262
Rubi steps
\begin {align*} \int \frac {9+x^4}{x^2 \left (9+x^2\right )} \, dx &=\int \left (1+\frac {1}{x^2}-\frac {10}{9+x^2}\right ) \, dx\\ &=-\frac {1}{x}+x-10 \int \frac {1}{9+x^2} \, dx\\ &=-\frac {1}{x}+x-\frac {10}{3} \tan ^{-1}\left (\frac {x}{3}\right )\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.01, size = 17, normalized size = 1.00 \begin {gather*} x-\frac {1}{x}-\frac {10}{3} \tan ^{-1}\left (\frac {x}{3}\right ) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {9+x^4}{x^2 \left (9+x^2\right )} \, dx \end {gather*}
Verification is not applicable to the result.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 1.62, size = 19, normalized size = 1.12 \begin {gather*} \frac {3 \, x^{2} - 10 \, x \arctan \left (\frac {1}{3} \, x\right ) - 3}{3 \, x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.30, size = 13, normalized size = 0.76 \begin {gather*} x - \frac {1}{x} - \frac {10}{3} \, \arctan \left (\frac {1}{3} \, x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.01, size = 14, normalized size = 0.82 \begin {gather*} x -\frac {10 \arctan \left (\frac {x}{3}\right )}{3}-\frac {1}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 2.04, size = 13, normalized size = 0.76 \begin {gather*} x - \frac {1}{x} - \frac {10}{3} \, \arctan \left (\frac {1}{3} \, x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.03, size = 13, normalized size = 0.76 \begin {gather*} x-\frac {10\,\mathrm {atan}\left (\frac {x}{3}\right )}{3}-\frac {1}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.11, size = 12, normalized size = 0.71 \begin {gather*} x - \frac {10 \operatorname {atan}{\left (\frac {x}{3} \right )}}{3} - \frac {1}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________