Optimal. Leaf size=19 \[ -\frac {(9-3 x)^2}{2 x}+\log ^2(9) \]
________________________________________________________________________________________
Rubi [A] time = 0.00, antiderivative size = 13, normalized size of antiderivative = 0.68, number of steps used = 3, number of rules used = 2, integrand size = 14, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.143, Rules used = {12, 14} \begin {gather*} -\frac {9 x}{2}-\frac {81}{2 x} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 12
Rule 14
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{2} \int \frac {81-9 x^2}{x^2} \, dx\\ &=\frac {1}{2} \int \left (-9+\frac {81}{x^2}\right ) \, dx\\ &=-\frac {81}{2 x}-\frac {9 x}{2}\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A] time = 0.00, size = 13, normalized size = 0.68 \begin {gather*} \frac {9}{2} \left (-\frac {9}{x}-x\right ) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.85, size = 10, normalized size = 0.53 \begin {gather*} -\frac {9 \, {\left (x^{2} + 9\right )}}{2 \, x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.14, size = 9, normalized size = 0.47 \begin {gather*} -\frac {9}{2} \, x - \frac {81}{2 \, x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.02, size = 10, normalized size = 0.53
method | result | size |
default | \(-\frac {9 x}{2}-\frac {81}{2 x}\) | \(10\) |
risch | \(-\frac {9 x}{2}-\frac {81}{2 x}\) | \(10\) |
gosper | \(-\frac {9 \left (x^{2}+9\right )}{2 x}\) | \(11\) |
norman | \(\frac {-\frac {81}{2}-\frac {9 x^{2}}{2}}{x}\) | \(12\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.37, size = 9, normalized size = 0.47 \begin {gather*} -\frac {9}{2} \, x - \frac {81}{2 \, x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.02, size = 10, normalized size = 0.53 \begin {gather*} -\frac {9\,\left (x^2+9\right )}{2\,x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.06, size = 10, normalized size = 0.53 \begin {gather*} - \frac {9 x}{2} - \frac {81}{2 x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________