Optimal. Leaf size=30 \[ -4+x-\log \left (x-\left (-3+x+x^2\right )^2 \log \left (\frac {e^{2 x}}{3+x}\right )\right ) \]
________________________________________________________________________________________
Rubi [F] time = 3.29, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \int \frac {-42+10 x+36 x^2-9 x^4-2 x^5+\left (45+27 x-29 x^2-17 x^3+x^4+x^5\right ) \log \left (\frac {e^{2 x}}{3+x}\right )}{-3 x-x^2+\left (27-9 x-21 x^2+x^3+5 x^4+x^5\right ) \log \left (\frac {e^{2 x}}{3+x}\right )} \, dx \end {gather*}
Verification is not applicable to the result.
[In]
[Out]
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (\frac {-5-3 x+x^2}{-3+x+x^2}+\frac {126-87 x-154 x^2+46 x^3+64 x^4-3 x^5-11 x^6-2 x^7}{(3+x) \left (-3+x+x^2\right ) \left (-x+9 \log \left (\frac {e^{2 x}}{3+x}\right )-6 x \log \left (\frac {e^{2 x}}{3+x}\right )-5 x^2 \log \left (\frac {e^{2 x}}{3+x}\right )+2 x^3 \log \left (\frac {e^{2 x}}{3+x}\right )+x^4 \log \left (\frac {e^{2 x}}{3+x}\right )\right )}\right ) \, dx\\ &=\int \frac {-5-3 x+x^2}{-3+x+x^2} \, dx+\int \frac {126-87 x-154 x^2+46 x^3+64 x^4-3 x^5-11 x^6-2 x^7}{(3+x) \left (-3+x+x^2\right ) \left (-x+9 \log \left (\frac {e^{2 x}}{3+x}\right )-6 x \log \left (\frac {e^{2 x}}{3+x}\right )-5 x^2 \log \left (\frac {e^{2 x}}{3+x}\right )+2 x^3 \log \left (\frac {e^{2 x}}{3+x}\right )+x^4 \log \left (\frac {e^{2 x}}{3+x}\right )\right )} \, dx\\ &=\int \left (1-\frac {2 (1+2 x)}{-3+x+x^2}\right ) \, dx+\int \frac {126-87 x-154 x^2+46 x^3+64 x^4-3 x^5-11 x^6-2 x^7}{(3+x) \left (3-x-x^2\right ) \left (x-\left (-3+x+x^2\right )^2 \log \left (\frac {e^{2 x}}{3+x}\right )\right )} \, dx\\ &=x-2 \int \frac {1+2 x}{-3+x+x^2} \, dx+\int \left (-\frac {21}{-x+9 \log \left (\frac {e^{2 x}}{3+x}\right )-6 x \log \left (\frac {e^{2 x}}{3+x}\right )-5 x^2 \log \left (\frac {e^{2 x}}{3+x}\right )+2 x^3 \log \left (\frac {e^{2 x}}{3+x}\right )+x^4 \log \left (\frac {e^{2 x}}{3+x}\right )}+\frac {10 x}{-x+9 \log \left (\frac {e^{2 x}}{3+x}\right )-6 x \log \left (\frac {e^{2 x}}{3+x}\right )-5 x^2 \log \left (\frac {e^{2 x}}{3+x}\right )+2 x^3 \log \left (\frac {e^{2 x}}{3+x}\right )+x^4 \log \left (\frac {e^{2 x}}{3+x}\right )}+\frac {9 x^2}{-x+9 \log \left (\frac {e^{2 x}}{3+x}\right )-6 x \log \left (\frac {e^{2 x}}{3+x}\right )-5 x^2 \log \left (\frac {e^{2 x}}{3+x}\right )+2 x^3 \log \left (\frac {e^{2 x}}{3+x}\right )+x^4 \log \left (\frac {e^{2 x}}{3+x}\right )}-\frac {3 x^3}{-x+9 \log \left (\frac {e^{2 x}}{3+x}\right )-6 x \log \left (\frac {e^{2 x}}{3+x}\right )-5 x^2 \log \left (\frac {e^{2 x}}{3+x}\right )+2 x^3 \log \left (\frac {e^{2 x}}{3+x}\right )+x^4 \log \left (\frac {e^{2 x}}{3+x}\right )}-\frac {2 x^4}{-x+9 \log \left (\frac {e^{2 x}}{3+x}\right )-6 x \log \left (\frac {e^{2 x}}{3+x}\right )-5 x^2 \log \left (\frac {e^{2 x}}{3+x}\right )+2 x^3 \log \left (\frac {e^{2 x}}{3+x}\right )+x^4 \log \left (\frac {e^{2 x}}{3+x}\right )}+\frac {9}{(3+x) \left (-x+9 \log \left (\frac {e^{2 x}}{3+x}\right )-6 x \log \left (\frac {e^{2 x}}{3+x}\right )-5 x^2 \log \left (\frac {e^{2 x}}{3+x}\right )+2 x^3 \log \left (\frac {e^{2 x}}{3+x}\right )+x^4 \log \left (\frac {e^{2 x}}{3+x}\right )\right )}+\frac {2 (-6+x)}{\left (-3+x+x^2\right ) \left (-x+9 \log \left (\frac {e^{2 x}}{3+x}\right )-6 x \log \left (\frac {e^{2 x}}{3+x}\right )-5 x^2 \log \left (\frac {e^{2 x}}{3+x}\right )+2 x^3 \log \left (\frac {e^{2 x}}{3+x}\right )+x^4 \log \left (\frac {e^{2 x}}{3+x}\right )\right )}\right ) \, dx\\ &=x-2 \log \left (3-x-x^2\right )-2 \int \frac {x^4}{-x+9 \log \left (\frac {e^{2 x}}{3+x}\right )-6 x \log \left (\frac {e^{2 x}}{3+x}\right )-5 x^2 \log \left (\frac {e^{2 x}}{3+x}\right )+2 x^3 \log \left (\frac {e^{2 x}}{3+x}\right )+x^4 \log \left (\frac {e^{2 x}}{3+x}\right )} \, dx+2 \int \frac {-6+x}{\left (-3+x+x^2\right ) \left (-x+9 \log \left (\frac {e^{2 x}}{3+x}\right )-6 x \log \left (\frac {e^{2 x}}{3+x}\right )-5 x^2 \log \left (\frac {e^{2 x}}{3+x}\right )+2 x^3 \log \left (\frac {e^{2 x}}{3+x}\right )+x^4 \log \left (\frac {e^{2 x}}{3+x}\right )\right )} \, dx-3 \int \frac {x^3}{-x+9 \log \left (\frac {e^{2 x}}{3+x}\right )-6 x \log \left (\frac {e^{2 x}}{3+x}\right )-5 x^2 \log \left (\frac {e^{2 x}}{3+x}\right )+2 x^3 \log \left (\frac {e^{2 x}}{3+x}\right )+x^4 \log \left (\frac {e^{2 x}}{3+x}\right )} \, dx+9 \int \frac {x^2}{-x+9 \log \left (\frac {e^{2 x}}{3+x}\right )-6 x \log \left (\frac {e^{2 x}}{3+x}\right )-5 x^2 \log \left (\frac {e^{2 x}}{3+x}\right )+2 x^3 \log \left (\frac {e^{2 x}}{3+x}\right )+x^4 \log \left (\frac {e^{2 x}}{3+x}\right )} \, dx+9 \int \frac {1}{(3+x) \left (-x+9 \log \left (\frac {e^{2 x}}{3+x}\right )-6 x \log \left (\frac {e^{2 x}}{3+x}\right )-5 x^2 \log \left (\frac {e^{2 x}}{3+x}\right )+2 x^3 \log \left (\frac {e^{2 x}}{3+x}\right )+x^4 \log \left (\frac {e^{2 x}}{3+x}\right )\right )} \, dx+10 \int \frac {x}{-x+9 \log \left (\frac {e^{2 x}}{3+x}\right )-6 x \log \left (\frac {e^{2 x}}{3+x}\right )-5 x^2 \log \left (\frac {e^{2 x}}{3+x}\right )+2 x^3 \log \left (\frac {e^{2 x}}{3+x}\right )+x^4 \log \left (\frac {e^{2 x}}{3+x}\right )} \, dx-21 \int \frac {1}{-x+9 \log \left (\frac {e^{2 x}}{3+x}\right )-6 x \log \left (\frac {e^{2 x}}{3+x}\right )-5 x^2 \log \left (\frac {e^{2 x}}{3+x}\right )+2 x^3 \log \left (\frac {e^{2 x}}{3+x}\right )+x^4 \log \left (\frac {e^{2 x}}{3+x}\right )} \, dx\\ &=x-2 \log \left (3-x-x^2\right )+2 \int \frac {-6+x}{\left (3-x-x^2\right ) \left (x-\left (-3+x+x^2\right )^2 \log \left (\frac {e^{2 x}}{3+x}\right )\right )} \, dx-2 \int \frac {x^4}{-x+\left (-3+x+x^2\right )^2 \log \left (\frac {e^{2 x}}{3+x}\right )} \, dx-3 \int \frac {x^3}{-x+\left (-3+x+x^2\right )^2 \log \left (\frac {e^{2 x}}{3+x}\right )} \, dx+9 \int \frac {1}{(-3-x) \left (x-\left (-3+x+x^2\right )^2 \log \left (\frac {e^{2 x}}{3+x}\right )\right )} \, dx+9 \int \frac {x^2}{-x+\left (-3+x+x^2\right )^2 \log \left (\frac {e^{2 x}}{3+x}\right )} \, dx+10 \int \frac {x}{-x+\left (-3+x+x^2\right )^2 \log \left (\frac {e^{2 x}}{3+x}\right )} \, dx-21 \int \frac {1}{-x+\left (-3+x+x^2\right )^2 \log \left (\frac {e^{2 x}}{3+x}\right )} \, dx\\ &=x-2 \log \left (3-x-x^2\right )-2 \int \frac {x^4}{-x+\left (-3+x+x^2\right )^2 \log \left (\frac {e^{2 x}}{3+x}\right )} \, dx+2 \int \left (-\frac {6}{\left (-3+x+x^2\right ) \left (-x+9 \log \left (\frac {e^{2 x}}{3+x}\right )-6 x \log \left (\frac {e^{2 x}}{3+x}\right )-5 x^2 \log \left (\frac {e^{2 x}}{3+x}\right )+2 x^3 \log \left (\frac {e^{2 x}}{3+x}\right )+x^4 \log \left (\frac {e^{2 x}}{3+x}\right )\right )}+\frac {x}{\left (-3+x+x^2\right ) \left (-x+9 \log \left (\frac {e^{2 x}}{3+x}\right )-6 x \log \left (\frac {e^{2 x}}{3+x}\right )-5 x^2 \log \left (\frac {e^{2 x}}{3+x}\right )+2 x^3 \log \left (\frac {e^{2 x}}{3+x}\right )+x^4 \log \left (\frac {e^{2 x}}{3+x}\right )\right )}\right ) \, dx-3 \int \frac {x^3}{-x+\left (-3+x+x^2\right )^2 \log \left (\frac {e^{2 x}}{3+x}\right )} \, dx+9 \int \frac {1}{(-3-x) \left (x-\left (-3+x+x^2\right )^2 \log \left (\frac {e^{2 x}}{3+x}\right )\right )} \, dx+9 \int \frac {x^2}{-x+\left (-3+x+x^2\right )^2 \log \left (\frac {e^{2 x}}{3+x}\right )} \, dx+10 \int \frac {x}{-x+\left (-3+x+x^2\right )^2 \log \left (\frac {e^{2 x}}{3+x}\right )} \, dx-21 \int \frac {1}{-x+\left (-3+x+x^2\right )^2 \log \left (\frac {e^{2 x}}{3+x}\right )} \, dx\\ &=x-2 \log \left (3-x-x^2\right )+2 \int \frac {x}{\left (-3+x+x^2\right ) \left (-x+9 \log \left (\frac {e^{2 x}}{3+x}\right )-6 x \log \left (\frac {e^{2 x}}{3+x}\right )-5 x^2 \log \left (\frac {e^{2 x}}{3+x}\right )+2 x^3 \log \left (\frac {e^{2 x}}{3+x}\right )+x^4 \log \left (\frac {e^{2 x}}{3+x}\right )\right )} \, dx-2 \int \frac {x^4}{-x+\left (-3+x+x^2\right )^2 \log \left (\frac {e^{2 x}}{3+x}\right )} \, dx-3 \int \frac {x^3}{-x+\left (-3+x+x^2\right )^2 \log \left (\frac {e^{2 x}}{3+x}\right )} \, dx+9 \int \frac {1}{(-3-x) \left (x-\left (-3+x+x^2\right )^2 \log \left (\frac {e^{2 x}}{3+x}\right )\right )} \, dx+9 \int \frac {x^2}{-x+\left (-3+x+x^2\right )^2 \log \left (\frac {e^{2 x}}{3+x}\right )} \, dx+10 \int \frac {x}{-x+\left (-3+x+x^2\right )^2 \log \left (\frac {e^{2 x}}{3+x}\right )} \, dx-12 \int \frac {1}{\left (-3+x+x^2\right ) \left (-x+9 \log \left (\frac {e^{2 x}}{3+x}\right )-6 x \log \left (\frac {e^{2 x}}{3+x}\right )-5 x^2 \log \left (\frac {e^{2 x}}{3+x}\right )+2 x^3 \log \left (\frac {e^{2 x}}{3+x}\right )+x^4 \log \left (\frac {e^{2 x}}{3+x}\right )\right )} \, dx-21 \int \frac {1}{-x+\left (-3+x+x^2\right )^2 \log \left (\frac {e^{2 x}}{3+x}\right )} \, dx\\ &=x-2 \log \left (3-x-x^2\right )+2 \int \frac {x}{\left (3-x-x^2\right ) \left (x-\left (-3+x+x^2\right )^2 \log \left (\frac {e^{2 x}}{3+x}\right )\right )} \, dx-2 \int \frac {x^4}{-x+\left (-3+x+x^2\right )^2 \log \left (\frac {e^{2 x}}{3+x}\right )} \, dx-3 \int \frac {x^3}{-x+\left (-3+x+x^2\right )^2 \log \left (\frac {e^{2 x}}{3+x}\right )} \, dx+9 \int \frac {1}{(-3-x) \left (x-\left (-3+x+x^2\right )^2 \log \left (\frac {e^{2 x}}{3+x}\right )\right )} \, dx+9 \int \frac {x^2}{-x+\left (-3+x+x^2\right )^2 \log \left (\frac {e^{2 x}}{3+x}\right )} \, dx+10 \int \frac {x}{-x+\left (-3+x+x^2\right )^2 \log \left (\frac {e^{2 x}}{3+x}\right )} \, dx-12 \int \frac {1}{\left (3-x-x^2\right ) \left (x-\left (-3+x+x^2\right )^2 \log \left (\frac {e^{2 x}}{3+x}\right )\right )} \, dx-21 \int \frac {1}{-x+\left (-3+x+x^2\right )^2 \log \left (\frac {e^{2 x}}{3+x}\right )} \, dx\\ &=x-2 \log \left (3-x-x^2\right )-2 \int \frac {x^4}{-x+\left (-3+x+x^2\right )^2 \log \left (\frac {e^{2 x}}{3+x}\right )} \, dx+2 \int \left (\frac {1+\frac {1}{\sqrt {13}}}{\left (-1-\sqrt {13}-2 x\right ) \left (x-\left (-3+x+x^2\right )^2 \log \left (\frac {e^{2 x}}{3+x}\right )\right )}+\frac {1-\frac {1}{\sqrt {13}}}{\left (-1+\sqrt {13}-2 x\right ) \left (x-\left (-3+x+x^2\right )^2 \log \left (\frac {e^{2 x}}{3+x}\right )\right )}\right ) \, dx-3 \int \frac {x^3}{-x+\left (-3+x+x^2\right )^2 \log \left (\frac {e^{2 x}}{3+x}\right )} \, dx+9 \int \frac {1}{(-3-x) \left (x-\left (-3+x+x^2\right )^2 \log \left (\frac {e^{2 x}}{3+x}\right )\right )} \, dx+9 \int \frac {x^2}{-x+\left (-3+x+x^2\right )^2 \log \left (\frac {e^{2 x}}{3+x}\right )} \, dx+10 \int \frac {x}{-x+\left (-3+x+x^2\right )^2 \log \left (\frac {e^{2 x}}{3+x}\right )} \, dx-12 \int \left (\frac {2}{\sqrt {13} \left (-1+\sqrt {13}-2 x\right ) \left (x-\left (-3+x+x^2\right )^2 \log \left (\frac {e^{2 x}}{3+x}\right )\right )}+\frac {2}{\sqrt {13} \left (1+\sqrt {13}+2 x\right ) \left (x-\left (-3+x+x^2\right )^2 \log \left (\frac {e^{2 x}}{3+x}\right )\right )}\right ) \, dx-21 \int \frac {1}{-x+\left (-3+x+x^2\right )^2 \log \left (\frac {e^{2 x}}{3+x}\right )} \, dx\\ &=x-2 \log \left (3-x-x^2\right )-2 \int \frac {x^4}{-x+\left (-3+x+x^2\right )^2 \log \left (\frac {e^{2 x}}{3+x}\right )} \, dx-3 \int \frac {x^3}{-x+\left (-3+x+x^2\right )^2 \log \left (\frac {e^{2 x}}{3+x}\right )} \, dx+9 \int \frac {1}{(-3-x) \left (x-\left (-3+x+x^2\right )^2 \log \left (\frac {e^{2 x}}{3+x}\right )\right )} \, dx+9 \int \frac {x^2}{-x+\left (-3+x+x^2\right )^2 \log \left (\frac {e^{2 x}}{3+x}\right )} \, dx+10 \int \frac {x}{-x+\left (-3+x+x^2\right )^2 \log \left (\frac {e^{2 x}}{3+x}\right )} \, dx-21 \int \frac {1}{-x+\left (-3+x+x^2\right )^2 \log \left (\frac {e^{2 x}}{3+x}\right )} \, dx-\frac {24 \int \frac {1}{\left (-1+\sqrt {13}-2 x\right ) \left (x-\left (-3+x+x^2\right )^2 \log \left (\frac {e^{2 x}}{3+x}\right )\right )} \, dx}{\sqrt {13}}-\frac {24 \int \frac {1}{\left (1+\sqrt {13}+2 x\right ) \left (x-\left (-3+x+x^2\right )^2 \log \left (\frac {e^{2 x}}{3+x}\right )\right )} \, dx}{\sqrt {13}}+\frac {1}{13} \left (2 \left (13-\sqrt {13}\right )\right ) \int \frac {1}{\left (-1+\sqrt {13}-2 x\right ) \left (x-\left (-3+x+x^2\right )^2 \log \left (\frac {e^{2 x}}{3+x}\right )\right )} \, dx+\frac {1}{13} \left (2 \left (13+\sqrt {13}\right )\right ) \int \frac {1}{\left (-1-\sqrt {13}-2 x\right ) \left (x-\left (-3+x+x^2\right )^2 \log \left (\frac {e^{2 x}}{3+x}\right )\right )} \, dx\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [B] time = 0.06, size = 217, normalized size = 7.23 \begin {gather*} x-\log \left (17 x-12 x^2-10 x^3+4 x^4+2 x^5+9 \log \left (\frac {1}{3+x}\right )-6 x \log \left (\frac {1}{3+x}\right )-5 x^2 \log \left (\frac {1}{3+x}\right )+2 x^3 \log \left (\frac {1}{3+x}\right )+x^4 \log \left (\frac {1}{3+x}\right )+9 \left (-2 x-\log \left (\frac {1}{3+x}\right )+\log \left (\frac {e^{2 x}}{3+x}\right )\right )-6 x \left (-2 x-\log \left (\frac {1}{3+x}\right )+\log \left (\frac {e^{2 x}}{3+x}\right )\right )-5 x^2 \left (-2 x-\log \left (\frac {1}{3+x}\right )+\log \left (\frac {e^{2 x}}{3+x}\right )\right )+2 x^3 \left (-2 x-\log \left (\frac {1}{3+x}\right )+\log \left (\frac {e^{2 x}}{3+x}\right )\right )+x^4 \left (-2 x-\log \left (\frac {1}{3+x}\right )+\log \left (\frac {e^{2 x}}{3+x}\right )\right )\right ) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [B] time = 0.55, size = 69, normalized size = 2.30 \begin {gather*} x - 2 \, \log \left (x^{2} + x - 3\right ) - \log \left (\frac {{\left (x^{4} + 2 \, x^{3} - 5 \, x^{2} - 6 \, x + 9\right )} \log \left (\frac {e^{\left (2 \, x\right )}}{x + 3}\right ) - x}{x^{4} + 2 \, x^{3} - 5 \, x^{2} - 6 \, x + 9}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [B] time = 0.23, size = 68, normalized size = 2.27 \begin {gather*} x - \log \left (-2 \, x^{5} + x^{4} \log \left (x + 3\right ) - 4 \, x^{4} + 2 \, x^{3} \log \left (x + 3\right ) + 10 \, x^{3} - 5 \, x^{2} \log \left (x + 3\right ) + 12 \, x^{2} - 6 \, x \log \left (x + 3\right ) - 17 \, x + 9 \, \log \left (x + 3\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [B] time = 0.29, size = 170, normalized size = 5.67
method | result | size |
default | \(x -\ln \left (2 x^{5}-\ln \left (3+x \right ) x^{4}+x^{4} \left (\ln \left (\frac {{\mathrm e}^{2 x}}{3+x}\right )-2 x +\ln \left (3+x \right )\right )+4 x^{4}-2 \ln \left (3+x \right ) x^{3}+2 x^{3} \left (\ln \left (\frac {{\mathrm e}^{2 x}}{3+x}\right )-2 x +\ln \left (3+x \right )\right )-10 x^{3}+5 \ln \left (3+x \right ) x^{2}-5 x^{2} \left (\ln \left (\frac {{\mathrm e}^{2 x}}{3+x}\right )-2 x +\ln \left (3+x \right )\right )-12 x^{2}+6 x \ln \left (3+x \right )-6 x \left (\ln \left (\frac {{\mathrm e}^{2 x}}{3+x}\right )-2 x +\ln \left (3+x \right )\right )-x +9 \ln \left (\frac {{\mathrm e}^{2 x}}{3+x}\right )\right )\) | \(170\) |
risch | \(x -2 \ln \left (x^{2}+x -3\right )-\ln \left (\ln \left ({\mathrm e}^{2 x}\right )-\frac {i \left (-2 i x -2 \pi \,x^{3} \mathrm {csgn}\left (i {\mathrm e}^{2 x}\right ) \mathrm {csgn}\left (\frac {i {\mathrm e}^{2 x}}{3+x}\right )^{2}+5 \pi \,x^{2} \mathrm {csgn}\left (i {\mathrm e}^{2 x}\right ) \mathrm {csgn}\left (\frac {i {\mathrm e}^{2 x}}{3+x}\right )^{2}+9 \pi \,\mathrm {csgn}\left (\frac {i}{3+x}\right ) \mathrm {csgn}\left (i {\mathrm e}^{2 x}\right ) \mathrm {csgn}\left (\frac {i {\mathrm e}^{2 x}}{3+x}\right )+6 \pi x \,\mathrm {csgn}\left (i {\mathrm e}^{2 x}\right ) \mathrm {csgn}\left (\frac {i {\mathrm e}^{2 x}}{3+x}\right )^{2}-\pi \,x^{4} \mathrm {csgn}\left (\frac {i}{3+x}\right ) \mathrm {csgn}\left (\frac {i {\mathrm e}^{2 x}}{3+x}\right )^{2}-2 \pi \,x^{3} \mathrm {csgn}\left (\frac {i}{3+x}\right ) \mathrm {csgn}\left (\frac {i {\mathrm e}^{2 x}}{3+x}\right )^{2}+5 \pi \,x^{2} \mathrm {csgn}\left (\frac {i}{3+x}\right ) \mathrm {csgn}\left (\frac {i {\mathrm e}^{2 x}}{3+x}\right )^{2}+6 \pi x \,\mathrm {csgn}\left (\frac {i}{3+x}\right ) \mathrm {csgn}\left (\frac {i {\mathrm e}^{2 x}}{3+x}\right )^{2}-\pi \,x^{4} \mathrm {csgn}\left (i {\mathrm e}^{2 x}\right ) \mathrm {csgn}\left (\frac {i {\mathrm e}^{2 x}}{3+x}\right )^{2}+2 \pi \,x^{3} \mathrm {csgn}\left (\frac {i}{3+x}\right ) \mathrm {csgn}\left (i {\mathrm e}^{2 x}\right ) \mathrm {csgn}\left (\frac {i {\mathrm e}^{2 x}}{3+x}\right )-5 \pi \,x^{2} \mathrm {csgn}\left (\frac {i}{3+x}\right ) \mathrm {csgn}\left (i {\mathrm e}^{2 x}\right ) \mathrm {csgn}\left (\frac {i {\mathrm e}^{2 x}}{3+x}\right )-6 \pi x \,\mathrm {csgn}\left (\frac {i}{3+x}\right ) \mathrm {csgn}\left (i {\mathrm e}^{2 x}\right ) \mathrm {csgn}\left (\frac {i {\mathrm e}^{2 x}}{3+x}\right )+\pi \,x^{4} \mathrm {csgn}\left (\frac {i}{3+x}\right ) \mathrm {csgn}\left (i {\mathrm e}^{2 x}\right ) \mathrm {csgn}\left (\frac {i {\mathrm e}^{2 x}}{3+x}\right )-18 i \ln \left (3+x \right )+9 \pi \mathrm {csgn}\left (\frac {i {\mathrm e}^{2 x}}{3+x}\right )^{3}-9 \pi \,\mathrm {csgn}\left (\frac {i}{3+x}\right ) \mathrm {csgn}\left (\frac {i {\mathrm e}^{2 x}}{3+x}\right )^{2}-9 \pi \,\mathrm {csgn}\left (i {\mathrm e}^{2 x}\right ) \mathrm {csgn}\left (\frac {i {\mathrm e}^{2 x}}{3+x}\right )^{2}+\pi \,x^{4} \mathrm {csgn}\left (\frac {i {\mathrm e}^{2 x}}{3+x}\right )^{3}+10 i x^{2} \ln \left (3+x \right )+12 i x \ln \left (3+x \right )-2 i x^{4} \ln \left (3+x \right )-4 i x^{3} \ln \left (3+x \right )+2 \pi \,x^{3} \mathrm {csgn}\left (\frac {i {\mathrm e}^{2 x}}{3+x}\right )^{3}-5 \pi \,x^{2} \mathrm {csgn}\left (\frac {i {\mathrm e}^{2 x}}{3+x}\right )^{3}-6 \pi x \mathrm {csgn}\left (\frac {i {\mathrm e}^{2 x}}{3+x}\right )^{3}\right )}{2 \left (x^{4}+2 x^{3}-5 x^{2}-6 x +9\right )}\right )\) | \(652\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [B] time = 0.75, size = 84, normalized size = 2.80 \begin {gather*} x - 2 \, \log \left (x^{2} + x - 3\right ) - \log \left (-\frac {2 \, x^{5} + 4 \, x^{4} - 10 \, x^{3} - 12 \, x^{2} - {\left (x^{4} + 2 \, x^{3} - 5 \, x^{2} - 6 \, x + 9\right )} \log \left (x + 3\right ) + 17 \, x}{x^{4} + 2 \, x^{3} - 5 \, x^{2} - 6 \, x + 9}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [F] time = 0.00, size = -1, normalized size = -0.03 \begin {gather*} -\int \frac {10\,x+36\,x^2-9\,x^4-2\,x^5+\ln \left (\frac {{\mathrm {e}}^{2\,x}}{x+3}\right )\,\left (x^5+x^4-17\,x^3-29\,x^2+27\,x+45\right )-42}{3\,x+x^2-\ln \left (\frac {{\mathrm {e}}^{2\,x}}{x+3}\right )\,\left (x^5+5\,x^4+x^3-21\,x^2-9\,x+27\right )} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.75, size = 42, normalized size = 1.40 \begin {gather*} x - \log {\left (- \frac {x}{x^{4} + 2 x^{3} - 5 x^{2} - 6 x + 9} + \log {\left (\frac {e^{2 x}}{x + 3} \right )} \right )} - 2 \log {\left (x^{2} + x - 3 \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________