/ / 2\\ / 2\
| \x /| \x /
acos\e / 2*x*e
- ------------------- - --------------------------
2 ___________
(x + 1)*log (x + 1) / 2
/ 2*x
\/ 1 - e *log(x + 1)
$$- \frac{2 x e^{x^{2}}}{\sqrt{- e^{2 x^{2}} + 1} \log{\left(x + 1 \right)}} - \frac{\operatorname{acos}{\left(e^{x^{2}} \right)}}{\left(x + 1\right) \log{\left(x + 1 \right)}^{2}}$$
/ 2\
| 2 2*x | / 2\
| 2 2*x *e | \x /
2*|1 + 2*x - ----------|*e / / 2\\
| 2| / 2 \ | \x /| / 2\
| 2*x | |1 + ----------|*acos\e / \x /
\ -1 + e / \ log(1 + x)/ 4*x*e
- ------------------------------- + ---------------------------- + ----------------------------------
___________ 2 ___________
/ 2 (1 + x) *log(1 + x) / 2
/ 2*x / 2*x
\/ 1 - e (1 + x)*\/ 1 - e *log(1 + x)
-----------------------------------------------------------------------------------------------------
log(1 + x)
$$\frac{- \frac{2 \cdot \left(- \frac{2 x^{2} e^{2 x^{2}}}{e^{2 x^{2}} - 1} + 2 x^{2} + 1\right) e^{x^{2}}}{\sqrt{- e^{2 x^{2}} + 1}} + \frac{4 x e^{x^{2}}}{\sqrt{- e^{2 x^{2}} + 1} \left(x + 1\right) \log{\left(x + 1 \right)}} + \frac{\left(1 + \frac{2}{\log{\left(x + 1 \right)}}\right) \operatorname{acos}{\left(e^{x^{2}} \right)}}{\left(x + 1\right)^{2} \log{\left(x + 1 \right)}}}{\log{\left(x + 1 \right)}}$$
/ / 2 2 2 \ \
| | 2*x 2 2*x 2 4*x | / 2\ / 2\ |
| | 2 3*e 8*x *e 6*x *e | \x / | 2 2*x | / 2\ |
| / / 2\\ 2*x*|3 + 2*x - ---------- - ---------- + -------------|*e | 2 2*x *e | \x / |
| / 3 3 \ | \x /| | 2 2 2| 3*|1 + 2*x - ----------|*e / 2\ |
| |1 + ---------- + -----------|*acos\e / | 2*x 2*x / 2\ | | 2| / 2 \ \x / |
| | log(1 + x) 2 | | -1 + e -1 + e | 2*x | | | 2*x | 3*x*|1 + ----------|*e |
| \ log (1 + x)/ \ \-1 + e / / \ -1 + e / \ log(1 + x)/ |
2*|- ------------------------------------------ - -------------------------------------------------------------- + ---------------------------------- - -----------------------------------|
| 3 ___________ ___________ ___________ |
| (1 + x) *log(1 + x) / 2 / 2 / 2 |
| / 2*x / 2*x 2 / 2*x |
\ \/ 1 - e (1 + x)*\/ 1 - e *log(1 + x) (1 + x) *\/ 1 - e *log(1 + x)/
--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
log(1 + x)
$$\frac{2 \left(- \frac{2 x \left(\frac{6 x^{2} e^{4 x^{2}}}{\left(e^{2 x^{2}} - 1\right)^{2}} - \frac{8 x^{2} e^{2 x^{2}}}{e^{2 x^{2}} - 1} + 2 x^{2} - \frac{3 e^{2 x^{2}}}{e^{2 x^{2}} - 1} + 3\right) e^{x^{2}}}{\sqrt{- e^{2 x^{2}} + 1}} - \frac{3 x \left(1 + \frac{2}{\log{\left(x + 1 \right)}}\right) e^{x^{2}}}{\sqrt{- e^{2 x^{2}} + 1} \left(x + 1\right)^{2} \log{\left(x + 1 \right)}} + \frac{3 \cdot \left(- \frac{2 x^{2} e^{2 x^{2}}}{e^{2 x^{2}} - 1} + 2 x^{2} + 1\right) e^{x^{2}}}{\sqrt{- e^{2 x^{2}} + 1} \left(x + 1\right) \log{\left(x + 1 \right)}} - \frac{\left(1 + \frac{3}{\log{\left(x + 1 \right)}} + \frac{3}{\log{\left(x + 1 \right)}^{2}}\right) \operatorname{acos}{\left(e^{x^{2}} \right)}}{\left(x + 1\right)^{3} \log{\left(x + 1 \right)}}\right)}{\log{\left(x + 1 \right)}}$$