Интеграл sqrt(x)*sin(x) (dx)
Решение
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1 / | | ___ | \/ x *sin(x) dx | / 0
$$\int_{0}^{1} \sqrt{x} \sin{\left (x \right )}\, dx$$
График
Ответ
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/ ___ \ 1 ___ ____ |\/ 2 | / 5*\/ 2 *\/ pi *fresnelc|------|*gamma(5/4) | | ____| | ___ 5*cos(1)*gamma(5/4) \\/ pi / | \/ x *sin(x) dx = - ------------------- + ------------------------------------------ | 4*gamma(9/4) 8*gamma(9/4) / 0
$$-{{\sqrt{\pi}\,\left(\left(\sqrt{2}\,i-\sqrt{2}\right)\,
\mathrm{erf}\left({{\sqrt{2}\,i+\sqrt{2}}\over{2}}\right)+\left(
\sqrt{2}\,i+\sqrt{2}\right)\,\mathrm{erf}\left({{\sqrt{2}\,i-\sqrt{2
}}\over{2}}\right)+\left(-\sqrt{2}\,i-\sqrt{2}\right)\,\mathrm{erf}
\left(\sqrt{-i}\right)+\left(\sqrt{2}\,i-\sqrt{2}\right)\,
\mathrm{erf}\left(\left(-1\right)^{{{1}\over{4}}}\right)\right)+16\,
\cos 1}\over{16}}$$
Численный ответ
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0.364221932032132
Ответ (Неопределённый)
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/ ___ ___\
___ ____ |\/ 2 *\/ x |
/ 5*\/ 2 *\/ pi *fresnelc|-----------|*gamma(5/4)
| ___ | ____ |
| ___ 5*\/ x *cos(x)*gamma(5/4) \ \/ pi /
| \/ x *sin(x) dx = C - ------------------------- + -----------------------------------------------
| 4*gamma(9/4) 8*gamma(9/4)
/
$$-{{16\,\sqrt{x}\,\cos x+\sqrt{\pi}\,\left(\left(\sqrt{2}\,i-\sqrt{2
}\right)\,\mathrm{erf}\left({{\left(\sqrt{2}\,i+\sqrt{2}\right)\,
\sqrt{x}}\over{2}}\right)+\left(\sqrt{2}\,i+\sqrt{2}\right)\,
\mathrm{erf}\left({{\left(\sqrt{2}\,i-\sqrt{2}\right)\,\sqrt{x}
}\over{2}}\right)+\left(-\sqrt{2}\,i-\sqrt{2}\right)\,\mathrm{erf}
\left(\sqrt{-i}\,\sqrt{x}\right)+\left(\sqrt{2}\,i-\sqrt{2}\right)\,
\mathrm{erf}\left(\left(-1\right)^{{{1}\over{4}}}\,\sqrt{x}\right)
\right)}\over{16}}$$