Интеграл sin(t^2) (dx)

$$int_{0}^{1} sin{left (t^{2} right )}, dt$$

/ ___
1 ___ ____ |/ 2 |
/ 3*/ 2 */ pi *fresnels|——|*gamma(3/4)
| | ____|
| / 2 / pi /
| sint / dt = ——————————————
| 8*gamma(7/4)
/
0

$${{sqrt{pi},left(left(sqrt{2},i+sqrt{2}right),mathrm{erf}
left({{sqrt{2},i+sqrt{2}}over{2}}right)+left(sqrt{2},i-
sqrt{2}right),mathrm{erf}left({{sqrt{2},i-sqrt{2}}over{2}}
right)+left(sqrt{2}-sqrt{2},iright),mathrm{erf}left(sqrt{-
i}right)+left(sqrt{2},i+sqrt{2}right),mathrm{erf}left(
left(-1right)^{{{1}over{4}}}right)right)}over{16}}$$

0.310268301723381

/ ___
___ ____ |t*/ 2 |
/ 3*/ 2 */ pi *fresnels|——-|*gamma(3/4)
| | ____|
| / 2 / pi /
| sint / dt = C + ——————————————-
| 8*gamma(7/4)
/

$${{sqrt{pi},left(left(sqrt{2},i+sqrt{2}right),mathrm{erf}
left({{left(sqrt{2},i+sqrt{2}right),t}over{2}}right)+left(
sqrt{2},i-sqrt{2}right),mathrm{erf}left({{left(sqrt{2},i-
sqrt{2}right),t}over{2}}right)+left(sqrt{2}-sqrt{2},i
right),mathrm{erf}left(sqrt{-i},tright)+left(sqrt{2},i+
sqrt{2}right),mathrm{erf}left(left(-1right)^{{{1}over{4}}},
tright)right)}over{16}}$$

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