Optimal. Leaf size=25 \[ -1-\frac {e^9 x}{4 \left (-5+x^2\right )}-\log (x)+\log \left (x^2\right ) \]
________________________________________________________________________________________
Rubi [A] time = 0.06, antiderivative size = 20, normalized size of antiderivative = 0.80, number of steps used = 5, number of rules used = 5, integrand size = 40, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.125, Rules used = {1594, 28, 1805, 21, 29} \begin {gather*} \frac {e^9 x}{4 \left (5-x^2\right )}+\log (x) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 21
Rule 28
Rule 29
Rule 1594
Rule 1805
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {100-40 x^2+4 x^4+e^9 \left (5 x+x^3\right )}{x \left (100-40 x^2+4 x^4\right )} \, dx\\ &=4 \int \frac {100-40 x^2+4 x^4+e^9 \left (5 x+x^3\right )}{x \left (-20+4 x^2\right )^2} \, dx\\ &=\frac {e^9 x}{4 \left (5-x^2\right )}+\frac {1}{10} \int \frac {-200+40 x^2}{x \left (-20+4 x^2\right )} \, dx\\ &=\frac {e^9 x}{4 \left (5-x^2\right )}+\int \frac {1}{x} \, dx\\ &=\frac {e^9 x}{4 \left (5-x^2\right )}+\log (x)\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A] time = 0.01, size = 18, normalized size = 0.72 \begin {gather*} -\frac {e^9 x}{4 \left (-5+x^2\right )}+\log (x) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.52, size = 23, normalized size = 0.92 \begin {gather*} -\frac {x e^{9} - 4 \, {\left (x^{2} - 5\right )} \log \relax (x)}{4 \, {\left (x^{2} - 5\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.16, size = 16, normalized size = 0.64 \begin {gather*} -\frac {x e^{9}}{4 \, {\left (x^{2} - 5\right )}} + \log \left ({\left | x \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.06, size = 16, normalized size = 0.64
method | result | size |
default | \(\ln \relax (x )-\frac {x \,{\mathrm e}^{9}}{4 \left (x^{2}-5\right )}\) | \(16\) |
norman | \(\ln \relax (x )-\frac {x \,{\mathrm e}^{9}}{4 \left (x^{2}-5\right )}\) | \(16\) |
risch | \(\ln \relax (x )-\frac {x \,{\mathrm e}^{9}}{4 \left (x^{2}-5\right )}\) | \(16\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.35, size = 15, normalized size = 0.60 \begin {gather*} -\frac {x e^{9}}{4 \, {\left (x^{2} - 5\right )}} + \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.08, size = 17, normalized size = 0.68 \begin {gather*} \ln \relax (x)-\frac {x\,{\mathrm {e}}^9}{4\,\left (x^2-5\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.22, size = 14, normalized size = 0.56 \begin {gather*} - \frac {x e^{9}}{4 x^{2} - 20} + \log {\relax (x )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________