Интеграл cos(4*x^2) (dx)
Решение
Вы ввели
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1 / | | / 2\ | cos\4*x / dx | / 0
$$\int_{0}^{1} \cos{\left (4 x^{2} \right )}\, dx$$
График
Ответ
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/ ___\ 1 ___ ____ |2*\/ 2 | / \/ 2 *\/ pi *fresnelc|-------|*gamma(1/4) | | ____| | / 2\ \ \/ pi / | cos\4*x / dx = ----------------------------------------- | 16*gamma(5/4) / 0
$$-{{\sqrt{\pi}\,\left(\left(\sqrt{2}\,i-\sqrt{2}\right)\,
\mathrm{erf}\left(\sqrt{2}\,i+\sqrt{2}\right)+\left(\sqrt{2}\,i+
\sqrt{2}\right)\,\mathrm{erf}\left(\sqrt{2}\,i-\sqrt{2}\right)+
\left(-\sqrt{2}\,i-\sqrt{2}\right)\,\mathrm{erf}\left(2\,\sqrt{-i}
\right)+\left(\sqrt{2}\,i-\sqrt{2}\right)\,\mathrm{erf}\left(2\,
\left(-1\right)^{{{1}\over{4}}}\right)\right)}\over{32}}$$
Ответ (Неопределённый)
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[pretty]
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/ ___\
___ ____ |2*x*\/ 2 |
/ \/ 2 *\/ pi *fresnelc|---------|*gamma(1/4)
| | ____ |
| / 2\ \ \/ pi /
| cos\4*x / dx = C + -------------------------------------------
| 16*gamma(5/4)
/
$$-{{\sqrt{\pi}\,\left(\left(\sqrt{2}\,i-\sqrt{2}\right)\,
\mathrm{erf}\left(\left(\sqrt{2}\,i+\sqrt{2}\right)\,x\right)+\left(
-\sqrt{2}\,i-\sqrt{2}\right)\,\mathrm{erf}\left(\left(\sqrt{2}-
\sqrt{2}\,i\right)\,x\right)+\left(-\sqrt{2}\,i-\sqrt{2}\right)\,
\mathrm{erf}\left(2\,\sqrt{-i}\,x\right)+\left(\sqrt{2}\,i-\sqrt{2}
\right)\,\mathrm{erf}\left(2\,\left(-1\right)^{{{1}\over{4}}}\,x
\right)\right)}\over{32}}$$