3 3 2 2 2 3 2
(x - 7) *(20 + 50*x) 3*(x - 7) *(5*x + 2) 3*(x - 7) *(5*x + 2) 10*(x - 7) *(5*x + 2)
-------------------- - --------------------- + --------------------- - -------------------------------------
3 5 4 5 3 5 ________________
x *asin (2*x + 1) x *asin (2*x + 1) x *asin (2*x + 1) 3 / 2 6
x *\/ 1 - (2*x + 1) *asin (2*x + 1)
$$\frac{\left(x - 7\right)^{3} \cdot \left(50 x + 20\right)}{x^{3} \operatorname{asin}^{5}{\left(2 x + 1 \right)}} + \frac{3 \left(x - 7\right)^{2} \left(5 x + 2\right)^{2}}{x^{3} \operatorname{asin}^{5}{\left(2 x + 1 \right)}} - \frac{3 \left(x - 7\right)^{3} \left(5 x + 2\right)^{2}}{x^{4} \operatorname{asin}^{5}{\left(2 x + 1 \right)}} - \frac{10 \left(x - 7\right)^{3} \left(5 x + 2\right)^{2}}{x^{3} \sqrt{- \left(2 x + 1\right)^{2} + 1} \operatorname{asin}^{6}{\left(2 x + 1 \right)}}$$
/ 2 2 / 1 + 2*x 6 \ \
| 10*(-7 + x) *(2 + 5*x) *|------------------- + -------------------------------| |
| | 3/2 / 2\ | |
| 2 2 2 2 2 2 |/ 2\ \-1 + (1 + 2*x) /*asin(1 + 2*x)| 2 2 |
| 2 2 30*(-7 + x) *(2 + 5*x) 9*(2 + 5*x) *(-7 + x) 6*(-7 + x) *(2 + 5*x) 100*(-7 + x) *(2 + 5*x) 30*(2 + 5*x) *(-7 + x) \\1 - (1 + 2*x) / / 30*(-7 + x) *(2 + 5*x) |
2*(-7 + x)*|3*(2 + 5*x) + 25*(-7 + x) + 30*(-7 + x)*(2 + 5*x) - ---------------------- - --------------------- + ---------------------- - --------------------------------- - --------------------------------- - ------------------------------------------------------------------------------- + -----------------------------------|
| x x 2 ________________ ________________ asin(1 + 2*x) ________________ |
| x / 2 / 2 / 2 |
\ \/ 1 - (1 + 2*x) *asin(1 + 2*x) \/ 1 - (1 + 2*x) *asin(1 + 2*x) x*\/ 1 - (1 + 2*x) *asin(1 + 2*x)/
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3 5
x *asin (1 + 2*x)
$$\frac{2 \left(x - 7\right) \left(- \frac{10 \left(x - 7\right)^{2} \left(5 x + 2\right)^{2} \cdot \left(\frac{6}{\left(\left(2 x + 1\right)^{2} - 1\right) \operatorname{asin}{\left(2 x + 1 \right)}} + \frac{2 x + 1}{\left(- \left(2 x + 1\right)^{2} + 1\right)^{\frac{3}{2}}}\right)}{\operatorname{asin}{\left(2 x + 1 \right)}} + 25 \left(x - 7\right)^{2} + 30 \left(x - 7\right) \left(5 x + 2\right) + 3 \left(5 x + 2\right)^{2} - \frac{30 \left(x - 7\right)^{2} \cdot \left(5 x + 2\right)}{x} - \frac{9 \left(x - 7\right) \left(5 x + 2\right)^{2}}{x} + \frac{6 \left(x - 7\right)^{2} \left(5 x + 2\right)^{2}}{x^{2}} - \frac{100 \left(x - 7\right)^{2} \cdot \left(5 x + 2\right)}{\sqrt{- \left(2 x + 1\right)^{2} + 1} \operatorname{asin}{\left(2 x + 1 \right)}} - \frac{30 \left(x - 7\right) \left(5 x + 2\right)^{2}}{\sqrt{- \left(2 x + 1\right)^{2} + 1} \operatorname{asin}{\left(2 x + 1 \right)}} + \frac{30 \left(x - 7\right)^{2} \left(5 x + 2\right)^{2}}{x \sqrt{- \left(2 x + 1\right)^{2} + 1} \operatorname{asin}{\left(2 x + 1 \right)}}\right)}{x^{3} \operatorname{asin}^{5}{\left(2 x + 1 \right)}}$$
/ / 2 \ \
| 3 / 1 + 2*x 6 \ 2 2 / 1 + 2*x 6 \ 3 2 | 1 3*(1 + 2*x) 42 18*(1 + 2*x) | 3 2 / 1 + 2*x 6 \ |
| 300*(-7 + x) *(2 + 5*x)*|------------------- + -------------------------------| 90*(-7 + x) *(2 + 5*x) *|------------------- + -------------------------------| 20*(-7 + x) *(2 + 5*x) *|------------------- + ------------------- + ---------------------------------- - --------------------------------| 90*(-7 + x) *(2 + 5*x) *|------------------- + -------------------------------| |
| | 3/2 / 2\ | | 3/2 / 2\ | | 3/2 5/2 3/2 2 | | 3/2 / 2\ | |
| 3 3 2 3 2 2 2 2 3 2 |/ 2\ \-1 + (1 + 2*x) /*asin(1 + 2*x)| 2 |/ 2\ \-1 + (1 + 2*x) /*asin(1 + 2*x)| |/ 2\ / 2\ / 2\ 2 / 2\ | 3 2 |/ 2\ \-1 + (1 + 2*x) /*asin(1 + 2*x)| 2 2 3 |
| 2 2 225*(-7 + x) 750*(-7 + x) 270*(-7 + x) *(2 + 5*x) 30*(-7 + x) *(2 + 5*x) 27*(2 + 5*x) *(-7 + x) 54*(-7 + x) *(2 + 5*x) 180*(-7 + x) *(2 + 5*x) 900*(-7 + x) *(2 + 5*x) \\1 - (1 + 2*x) / / 90*(2 + 5*x) *(-7 + x) \\1 - (1 + 2*x) / / \\1 - (1 + 2*x) / \1 - (1 + 2*x) / \1 - (1 + 2*x) / *asin (1 + 2*x) \-1 + (1 + 2*x) / *asin(1 + 2*x)/ 180*(-7 + x) *(2 + 5*x) \\1 - (1 + 2*x) / / 270*(-7 + x) *(2 + 5*x) 900*(-7 + x) *(2 + 5*x) |
2*|3*(2 + 5*x) + 225*(-7 + x) - ------------- + 90*(-7 + x)*(2 + 5*x) - --------------------------------- - ----------------------- - ----------------------- - ---------------------- + ----------------------- + ----------------------- - --------------------------------- - ------------------------------------------------------------------------------- - --------------------------------- - ------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------------- - ------------------------------------ + ------------------------------------------------------------------------------- + ----------------------------------- + -----------------------------------|
| x ________________ x 3 x 2 2 ________________ asin(1 + 2*x) ________________ asin(1 + 2*x) asin(1 + 2*x) ________________ x*asin(1 + 2*x) ________________ ________________ |
| / 2 x x x / 2 / 2 2 / 2 / 2 / 2 |
\ \/ 1 - (1 + 2*x) *asin(1 + 2*x) \/ 1 - (1 + 2*x) *asin(1 + 2*x) \/ 1 - (1 + 2*x) *asin(1 + 2*x) x *\/ 1 - (1 + 2*x) *asin(1 + 2*x) x*\/ 1 - (1 + 2*x) *asin(1 + 2*x) x*\/ 1 - (1 + 2*x) *asin(1 + 2*x)/
--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
3 5
x *asin (1 + 2*x)
$$\frac{2 \left(- \frac{20 \left(x - 7\right)^{3} \left(5 x + 2\right)^{2} \left(- \frac{18 \cdot \left(2 x + 1\right)}{\left(\left(2 x + 1\right)^{2} - 1\right)^{2} \operatorname{asin}{\left(2 x + 1 \right)}} + \frac{1}{\left(- \left(2 x + 1\right)^{2} + 1\right)^{\frac{3}{2}}} + \frac{3 \left(2 x + 1\right)^{2}}{\left(- \left(2 x + 1\right)^{2} + 1\right)^{\frac{5}{2}}} + \frac{42}{\left(- \left(2 x + 1\right)^{2} + 1\right)^{\frac{3}{2}} \operatorname{asin}^{2}{\left(2 x + 1 \right)}}\right)}{\operatorname{asin}{\left(2 x + 1 \right)}} - \frac{300 \left(x - 7\right)^{3} \cdot \left(5 x + 2\right) \left(\frac{6}{\left(\left(2 x + 1\right)^{2} - 1\right) \operatorname{asin}{\left(2 x + 1 \right)}} + \frac{2 x + 1}{\left(- \left(2 x + 1\right)^{2} + 1\right)^{\frac{3}{2}}}\right)}{\operatorname{asin}{\left(2 x + 1 \right)}} - \frac{90 \left(x - 7\right)^{2} \left(5 x + 2\right)^{2} \cdot \left(\frac{6}{\left(\left(2 x + 1\right)^{2} - 1\right) \operatorname{asin}{\left(2 x + 1 \right)}} + \frac{2 x + 1}{\left(- \left(2 x + 1\right)^{2} + 1\right)^{\frac{3}{2}}}\right)}{\operatorname{asin}{\left(2 x + 1 \right)}} + \frac{90 \left(x - 7\right)^{3} \left(5 x + 2\right)^{2} \cdot \left(\frac{6}{\left(\left(2 x + 1\right)^{2} - 1\right) \operatorname{asin}{\left(2 x + 1 \right)}} + \frac{2 x + 1}{\left(- \left(2 x + 1\right)^{2} + 1\right)^{\frac{3}{2}}}\right)}{x \operatorname{asin}{\left(2 x + 1 \right)}} + 225 \left(x - 7\right)^{2} + 90 \left(x - 7\right) \left(5 x + 2\right) + 3 \left(5 x + 2\right)^{2} - \frac{225 \left(x - 7\right)^{3}}{x} - \frac{270 \left(x - 7\right)^{2} \cdot \left(5 x + 2\right)}{x} - \frac{27 \left(x - 7\right) \left(5 x + 2\right)^{2}}{x} + \frac{180 \left(x - 7\right)^{3} \cdot \left(5 x + 2\right)}{x^{2}} + \frac{54 \left(x - 7\right)^{2} \left(5 x + 2\right)^{2}}{x^{2}} - \frac{30 \left(x - 7\right)^{3} \left(5 x + 2\right)^{2}}{x^{3}} - \frac{750 \left(x - 7\right)^{3}}{\sqrt{- \left(2 x + 1\right)^{2} + 1} \operatorname{asin}{\left(2 x + 1 \right)}} - \frac{900 \left(x - 7\right)^{2} \cdot \left(5 x + 2\right)}{\sqrt{- \left(2 x + 1\right)^{2} + 1} \operatorname{asin}{\left(2 x + 1 \right)}} - \frac{90 \left(x - 7\right) \left(5 x + 2\right)^{2}}{\sqrt{- \left(2 x + 1\right)^{2} + 1} \operatorname{asin}{\left(2 x + 1 \right)}} + \frac{900 \left(x - 7\right)^{3} \cdot \left(5 x + 2\right)}{x \sqrt{- \left(2 x + 1\right)^{2} + 1} \operatorname{asin}{\left(2 x + 1 \right)}} + \frac{270 \left(x - 7\right)^{2} \left(5 x + 2\right)^{2}}{x \sqrt{- \left(2 x + 1\right)^{2} + 1} \operatorname{asin}{\left(2 x + 1 \right)}} - \frac{180 \left(x - 7\right)^{3} \left(5 x + 2\right)^{2}}{x^{2} \sqrt{- \left(2 x + 1\right)^{2} + 1} \operatorname{asin}{\left(2 x + 1 \right)}}\right)}{x^{3} \operatorname{asin}^{5}{\left(2 x + 1 \right)}}$$