Optimal. Leaf size=18 \[ -4+\log \left (-e^5-\frac {1}{x}+x+x^2\right ) \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.07, antiderivative size = 23, normalized size of antiderivative = 1.28, number of steps
used = 3, number of rules used = 2, integrand size = 34, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.059, Rules used = {2099, 1601}
\begin {gather*} \log \left (-x^3-x^2+e^5 x+1\right )-\log (x) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 1601
Rule 2099
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-\frac {1}{x}+\frac {e^5-2 x-3 x^2}{1+e^5 x-x^2-x^3}\right ) \, dx\\ &=-\log (x)+\int \frac {e^5-2 x-3 x^2}{1+e^5 x-x^2-x^3} \, dx\\ &=-\log (x)+\log \left (1+e^5 x-x^2-x^3\right )\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A]
time = 0.02, size = 23, normalized size = 1.28 \begin {gather*} -\log (x)+\log \left (1+e^5 x-x^2-x^3\right ) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.62, size = 20, normalized size = 1.11
method | result | size |
default | \(\ln \left (x^{3}-x \,{\mathrm e}^{5}+x^{2}-1\right )-\ln \left (x \right )\) | \(20\) |
risch | \(\ln \left (x^{3}-x \,{\mathrm e}^{5}+x^{2}-1\right )-\ln \left (x \right )\) | \(20\) |
norman | \(-\ln \left (x \right )+\ln \left (-x^{3}+x \,{\mathrm e}^{5}-x^{2}+1\right )\) | \(23\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.26, size = 19, normalized size = 1.06 \begin {gather*} \log \left (x^{3} + x^{2} - x e^{5} - 1\right ) - \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.37, size = 19, normalized size = 1.06 \begin {gather*} \log \left (x^{3} + x^{2} - x e^{5} - 1\right ) - \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.35, size = 17, normalized size = 0.94 \begin {gather*} - \log {\left (x \right )} + \log {\left (x^{3} + x^{2} - x e^{5} - 1 \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 0.42, size = 21, normalized size = 1.17 \begin {gather*} \log \left ({\left | x^{3} + x^{2} - x e^{5} - 1 \right |}\right ) - \log \left ({\left | x \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 7.70, size = 19, normalized size = 1.06 \begin {gather*} \ln \left (x^3+x^2-{\mathrm {e}}^5\,x-1\right )-\ln \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________