/ 2 \
| 1 x |
40*|--------------- + ------------------------------|
| ________ 2 |
| / 2 / ________\ ________|
|1 + \/ 1 - x | / 2 | / 2 |
\ \1 + \/ 1 - x / *\/ 1 - x /
-----------------------------------------------------
2
x
1 + ------------------
2
/ ________\
| / 2 |
\1 + \/ 1 - x /
$$\frac{40 \left(\frac{x^{2}}{\sqrt{- x^{2} + 1} \left(\sqrt{- x^{2} + 1} + 1\right)^{2}} + \frac{1}{\sqrt{- x^{2} + 1} + 1}\right)}{\frac{x^{2}}{\left(\sqrt{- x^{2} + 1} + 1\right)^{2}} + 1}$$
/ 2 \
| / 2 \ |
| | x | |
| 2*|1 + -----------------------------| |
| | / ________\ ________| |
| 2 2 | | / 2 | / 2 | |
| 3 x 2*x \ \1 + \/ 1 - x /*\/ 1 - x / |
-40*x*|- ----------- - ----------- + --------------------------- + ------------------------------------------|
| ________ 3/2 / ________\ / ________\ / 2 \|
| / 2 / 2\ | / 2 | / 2\ | / 2 | | x ||
| \/ 1 - x \1 - x / \1 + \/ 1 - x /*\-1 + x / \1 + \/ 1 - x /*|1 + ------------------||
| | 2||
| | / ________\ ||
| | | / 2 | ||
\ \ \1 + \/ 1 - x / //
--------------------------------------------------------------------------------------------------------------
2
/ ________\ / 2 \
| / 2 | | x |
\1 + \/ 1 - x / *|1 + ------------------|
| 2|
| / ________\ |
| | / 2 | |
\ \1 + \/ 1 - x / /
$$- \frac{40 x \left(\frac{2 x^{2}}{\left(x^{2} - 1\right) \left(\sqrt{- x^{2} + 1} + 1\right)} + \frac{2 \left(\frac{x^{2}}{\sqrt{- x^{2} + 1} \left(\sqrt{- x^{2} + 1} + 1\right)} + 1\right)^{2}}{\left(\frac{x^{2}}{\left(\sqrt{- x^{2} + 1} + 1\right)^{2}} + 1\right) \left(\sqrt{- x^{2} + 1} + 1\right)} - \frac{x^{2}}{\left(- x^{2} + 1\right)^{\frac{3}{2}}} - \frac{3}{\sqrt{- x^{2} + 1}}\right)}{\left(\frac{x^{2}}{\left(\sqrt{- x^{2} + 1} + 1\right)^{2}} + 1\right) \left(\sqrt{- x^{2} + 1} + 1\right)^{2}}$$
/ / 2 \ / 4 4 2 \ 3 \
| | x | | x 3*x 5*x | / 2 \ / 2 \ / 2 2 \|
| 2*|1 + -----------------------------|*|1 + ----------------------------- - ---------------------------- + -----------------------------| 2 | x | 2 | x | | 3 x 2*x ||
| | / ________\ ________| | / ________\ 3/2 2 / ________\ ________| 8*x *|1 + -----------------------------| 4*x *|1 + -----------------------------|*|----------- + ----------- - ---------------------------||
| | | / 2 | / 2 | | | / 2 | / 2\ / ________\ | / 2 | / 2 | | / ________\ ________| | / ________\ ________| | ________ 3/2 / ________\ ||
| 4 2 2 4 4 \ \1 + \/ 1 - x /*\/ 1 - x / | \1 + \/ 1 - x /*\1 - x / | / 2 | / 2\ \1 + \/ 1 - x /*\/ 1 - x | | | / 2 | / 2 | | | / 2 | / 2 | | / 2 / 2\ | / 2 | / 2\||
| 3 3*x 6*x 12*x 6*x 6*x \ \1 + \/ 1 - x / *\-1 + x / / \ \1 + \/ 1 - x /*\/ 1 - x / \ \1 + \/ 1 - x /*\/ 1 - x / \\/ 1 - x \1 - x / \1 + \/ 1 - x /*\-1 + x //|
40*|----------- + ----------- + ----------- - --------------------------- + ---------------------------- + ------------------------------ - ---------------------------------------------------------------------------------------------------------------------------------------- + -------------------------------------------- - --------------------------------------------------------------------------------------------------|
| ________ 5/2 3/2 / ________\ / ________\ 2 2 / ________\ / 2 \ 3 2 2 |
| / 2 / 2\ / 2\ | / 2 | / 2\ | / 2 | / 2\ / ________\ 3/2 | / 2 | | x | / ________\ / 2 \ / ________\ / 2 \ |
|\/ 1 - x \1 - x / \1 - x / \1 + \/ 1 - x /*\-1 + x / \1 + \/ 1 - x /*\-1 + x / | / 2 | / 2\ \1 + \/ 1 - x /*|1 + ------------------| | / 2 | | x | | / 2 | | x | |
| \1 + \/ 1 - x / *\1 - x / | 2| \1 + \/ 1 - x / *|1 + ------------------| \1 + \/ 1 - x / *|1 + ------------------| |
| | / ________\ | | 2| | 2| |
| | | / 2 | | | / ________\ | | / ________\ | |
| \ \1 + \/ 1 - x / / | | / 2 | | | | / 2 | | |
\ \ \1 + \/ 1 - x / / \ \1 + \/ 1 - x / / /
-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
2
/ ________\ / 2 \
| / 2 | | x |
\1 + \/ 1 - x / *|1 + ------------------|
| 2|
| / ________\ |
| | / 2 | |
\ \1 + \/ 1 - x / /
$$\frac{40 \cdot \left(\frac{6 x^{4}}{\left(x^{2} - 1\right)^{2} \left(\sqrt{- x^{2} + 1} + 1\right)} - \frac{4 x^{2} \left(\frac{x^{2}}{\sqrt{- x^{2} + 1} \left(\sqrt{- x^{2} + 1} + 1\right)} + 1\right) \left(- \frac{2 x^{2}}{\left(x^{2} - 1\right) \left(\sqrt{- x^{2} + 1} + 1\right)} + \frac{x^{2}}{\left(- x^{2} + 1\right)^{\frac{3}{2}}} + \frac{3}{\sqrt{- x^{2} + 1}}\right)}{\left(\frac{x^{2}}{\left(\sqrt{- x^{2} + 1} + 1\right)^{2}} + 1\right) \left(\sqrt{- x^{2} + 1} + 1\right)^{2}} + \frac{8 x^{2} \left(\frac{x^{2}}{\sqrt{- x^{2} + 1} \left(\sqrt{- x^{2} + 1} + 1\right)} + 1\right)^{3}}{\left(\frac{x^{2}}{\left(\sqrt{- x^{2} + 1} + 1\right)^{2}} + 1\right)^{2} \left(\sqrt{- x^{2} + 1} + 1\right)^{3}} - \frac{12 x^{2}}{\left(x^{2} - 1\right) \left(\sqrt{- x^{2} + 1} + 1\right)} - \frac{2 \left(\frac{x^{2}}{\sqrt{- x^{2} + 1} \left(\sqrt{- x^{2} + 1} + 1\right)} + 1\right) \left(- \frac{3 x^{4}}{\left(x^{2} - 1\right) \left(\sqrt{- x^{2} + 1} + 1\right)^{2}} + \frac{x^{4}}{\left(- x^{2} + 1\right)^{\frac{3}{2}} \left(\sqrt{- x^{2} + 1} + 1\right)} + \frac{5 x^{2}}{\sqrt{- x^{2} + 1} \left(\sqrt{- x^{2} + 1} + 1\right)} + 1\right)}{\left(\frac{x^{2}}{\left(\sqrt{- x^{2} + 1} + 1\right)^{2}} + 1\right) \left(\sqrt{- x^{2} + 1} + 1\right)} + \frac{6 x^{4}}{\left(- x^{2} + 1\right)^{\frac{3}{2}} \left(\sqrt{- x^{2} + 1} + 1\right)^{2}} + \frac{3 x^{4}}{\left(- x^{2} + 1\right)^{\frac{5}{2}}} + \frac{6 x^{2}}{\left(- x^{2} + 1\right)^{\frac{3}{2}}} + \frac{3}{\sqrt{- x^{2} + 1}}\right)}{\left(\frac{x^{2}}{\left(\sqrt{- x^{2} + 1} + 1\right)^{2}} + 1\right) \left(\sqrt{- x^{2} + 1} + 1\right)^{2}}$$