Optimal. Leaf size=22 \[ \frac {x \left (5+x^2\right ) \left (3+e^4+x+\log (3)\right )}{x+x^2} \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.05, antiderivative size = 28, normalized size of antiderivative = 1.27, number of steps
used = 4, number of rules used = 3, integrand size = 49, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.061, Rules used = {6, 27, 1864}
\begin {gather*} (x+1)^2+x \left (e^4+\log (3)\right )+\frac {6 \left (2+e^4+\log (3)\right )}{x+1} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 6
Rule 27
Rule 1864
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-10+6 x+6 x^2+2 x^3+\left (-5+2 x+x^2\right ) \left (e^4+\log (3)\right )}{1+2 x+x^2} \, dx\\ &=\int \frac {-10+6 x+6 x^2+2 x^3+\left (-5+2 x+x^2\right ) \left (e^4+\log (3)\right )}{(1+x)^2} \, dx\\ &=\int \left (e^4+2 (1+x)+\log (3)-\frac {6 \left (2+e^4+\log (3)\right )}{(1+x)^2}\right ) \, dx\\ &=(1+x)^2+x \left (e^4+\log (3)\right )+\frac {6 \left (2+e^4+\log (3)\right )}{1+x}\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A]
time = 0.04, size = 27, normalized size = 1.23 \begin {gather*} x^2+x \left (2+e^4+\log (3)\right )+\frac {6 \left (2+e^4+\log (3)\right )}{1+x} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 1.37, size = 33, normalized size = 1.50
method | result | size |
norman | \(\frac {x^{3}+\left (\ln \left (3\right )+{\mathrm e}^{4}+3\right ) x^{2}+10+5 \ln \left (3\right )+5 \,{\mathrm e}^{4}}{x +1}\) | \(30\) |
default | \(x^{2}+2 x +x \ln \left (3\right )+x \,{\mathrm e}^{4}-\frac {-12-6 \ln \left (3\right )-6 \,{\mathrm e}^{4}}{x +1}\) | \(33\) |
gosper | \(\frac {x^{2} \ln \left (3\right )+x^{2} {\mathrm e}^{4}+x^{3}+3 x^{2}+5 \ln \left (3\right )+5 \,{\mathrm e}^{4}+10}{x +1}\) | \(37\) |
risch | \(x \ln \left (3\right )+x \,{\mathrm e}^{4}+x^{2}+2 x +\frac {6 \ln \left (3\right )}{x +1}+\frac {6 \,{\mathrm e}^{4}}{x +1}+\frac {12}{x +1}\) | \(41\) |
meijerg | \(-\frac {x \left (-2 x^{2}+6 x +12\right )}{2 \left (x +1\right )}+6 \ln \left (x +1\right )+\left (2 \ln \left (3\right )+2 \,{\mathrm e}^{4}+6\right ) \left (-\frac {x}{x +1}+\ln \left (x +1\right )\right )+\left (\ln \left (3\right )+{\mathrm e}^{4}+6\right ) \left (\frac {x \left (6+3 x \right )}{3 x +3}-2 \ln \left (x +1\right )\right )-\frac {5 \ln \left (3\right ) x}{x +1}-\frac {5 \,{\mathrm e}^{4} x}{x +1}-\frac {10 x}{x +1}\) | \(105\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.29, size = 25, normalized size = 1.14 \begin {gather*} x^{2} + x {\left (e^{4} + \log \left (3\right ) + 2\right )} + \frac {6 \, {\left (e^{4} + \log \left (3\right ) + 2\right )}}{x + 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.35, size = 37, normalized size = 1.68 \begin {gather*} \frac {x^{3} + 3 \, x^{2} + {\left (x^{2} + x + 6\right )} e^{4} + {\left (x^{2} + x + 6\right )} \log \left (3\right ) + 2 \, x + 12}{x + 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.08, size = 27, normalized size = 1.23 \begin {gather*} x^{2} + x \left (\log {\left (3 \right )} + 2 + e^{4}\right ) + \frac {6 \log {\left (3 \right )} + 12 + 6 e^{4}}{x + 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 0.40, size = 28, normalized size = 1.27 \begin {gather*} x^{2} + x e^{4} + x \log \left (3\right ) + 2 \, x + \frac {6 \, {\left (e^{4} + \log \left (3\right ) + 2\right )}}{x + 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 3.31, size = 26, normalized size = 1.18 \begin {gather*} x\,\left ({\mathrm {e}}^4+\ln \left (3\right )+2\right )+\frac {6\,{\mathrm {e}}^4+\ln \left (729\right )+12}{x+1}+x^2 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________