Интеграл sin(x+x^2) (dx)

Вы ввели

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$$\int_{0}^{1} \sin{\left (x^{2} + x \right )}\, dx$$

Ответ

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$${{\sqrt{\pi}\,\left(\left(\left(\sqrt{2}\,i-\sqrt{2}\right)\,\sin \left({{1}\over{4}}\right)+\left(\sqrt{2}\,i+\sqrt{2}\right)\,\cos \left({{1}\over{4}}\right)\right)\,\mathrm{erf}\left({{3\,i}\over{ \sqrt{2}\,i+\sqrt{2}}}\right)+\left(\left(-\sqrt{2}\,i-\sqrt{2} \right)\,\sin \left({{1}\over{4}}\right)+\left(\sqrt{2}-\sqrt{2}\,i \right)\,\cos \left({{1}\over{4}}\right)\right)\,\mathrm{erf}\left( {{3\,i}\over{\sqrt{2}\,i-\sqrt{2}}}\right)+\left(\left(\sqrt{2}\,i+ \sqrt{2}\right)\,\sin \left({{1}\over{4}}\right)+\left(\sqrt{2}\,i- \sqrt{2}\right)\,\cos \left({{1}\over{4}}\right)\right)\, \mathrm{erf}\left({{3\,i}\over{2\,\sqrt{-i}}}\right)+\left(\left( \sqrt{2}\,i-\sqrt{2}\right)\,\sin \left({{1}\over{4}}\right)+\left( \sqrt{2}\,i+\sqrt{2}\right)\,\cos \left({{1}\over{4}}\right)\right) \,\mathrm{erf}\left({{3\,i}\over{2\,\left(-1\right)^{{{1}\over{4}}} }}\right)\right)}\over{16}}-{{\sqrt{\pi}\,\left(\left(\left(\sqrt{2} \,i-\sqrt{2}\right)\,\sin \left({{1}\over{4}}\right)+\left(\sqrt{2} \,i+\sqrt{2}\right)\,\cos \left({{1}\over{4}}\right)\right)\, \mathrm{erf}\left({{i}\over{\sqrt{2}\,i+\sqrt{2}}}\right)+\left( \left(-\sqrt{2}\,i-\sqrt{2}\right)\,\sin \left({{1}\over{4}}\right)+ \left(\sqrt{2}-\sqrt{2}\,i\right)\,\cos \left({{1}\over{4}}\right) \right)\,\mathrm{erf}\left({{i}\over{\sqrt{2}\,i-\sqrt{2}}}\right)+ \left(\left(\sqrt{2}\,i+\sqrt{2}\right)\,\sin \left({{1}\over{4}} \right)+\left(\sqrt{2}\,i-\sqrt{2}\right)\,\cos \left({{1}\over{4}} \right)\right)\,\mathrm{erf}\left({{i}\over{2\,\sqrt{-i}}}\right)+ \left(\left(\sqrt{2}\,i-\sqrt{2}\right)\,\sin \left({{1}\over{4}} \right)+\left(\sqrt{2}\,i+\sqrt{2}\right)\,\cos \left({{1}\over{4}} \right)\right)\,\mathrm{erf}\left({{i}\over{2\,\left(-1\right)^{{{1 }\over{4}}}}}\right)\right)}\over{16}}$$

Численный ответ

0.614321979370631

Ответ (Неопределённый)

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