Дано
$$frac{1}{sqrt{2}} {atan}{left (frac{1}{sqrt{2}} sqrt{2 x – 1} right )}$$
Подстановка условия
$$frac{1}{sqrt{2}} {atan}{left (frac{1}{sqrt{2}} sqrt{2 x – 1} right )}$$
atan(sqrt(2*(-3/2) – 1)/sqrt(2))/sqrt(2)
$$frac{1}{sqrt{2}} {atan}{left (frac{1}{sqrt{2}} sqrt{2 (-3/2) – 1} right )}$$
atan(sqrt(2*(-3)/2 – 1)/sqrt(2))/sqrt(2)
$$frac{1}{sqrt{2}} {atan}{left (frac{1}{sqrt{2}} sqrt{frac{-6}{2} – 1} right )}$$
i*sqrt(2)*atanh(sqrt(2))/2
$$frac{sqrt{2} i}{2} {atanh}{left (sqrt{2} right )}$$
Степени
$$frac{sqrt{2}}{2} {atan}{left (frac{1}{2} sqrt{4 x – 2} right )}$$
/ ___ __________
___ |/ 2 */ -1 + 2*x |
/ 2 *atan|——————|
2 /
——————————
2
$$frac{sqrt{2}}{2} {atan}{left (frac{sqrt{2}}{2} sqrt{2 x – 1} right )}$$
Численный ответ
0.707106781186547*atan(sqrt(2*x – 1)/sqrt(2))
Рациональный знаменатель
$$frac{sqrt{2}}{2} {atan}{left (frac{sqrt{2}}{2} sqrt{2 x – 1} right )}$$
Объединение рациональных выражений
$$frac{sqrt{2}}{2} {atan}{left (frac{sqrt{2}}{2} sqrt{2 x – 1} right )}$$
Общее упрощение
/ ___ __________
___ |/ 2 */ -1 + 2*x |
/ 2 *atan|——————|
2 /
——————————
2
$$frac{sqrt{2}}{2} {atan}{left (frac{sqrt{2}}{2} sqrt{2 x – 1} right )}$$
Соберем выражение
$$frac{sqrt{2}}{2} {atan}{left (frac{1}{sqrt{2}} sqrt{2 x – 1} right )}$$
Общий знаменатель
/ ___ __________
___ |/ 2 */ -1 + 2*x |
/ 2 *atan|——————|
2 /
——————————
2
$$frac{sqrt{2}}{2} {atan}{left (frac{sqrt{2}}{2} sqrt{2 x – 1} right )}$$
Комбинаторика
/ ___ __________
___ |/ 2 */ -1 + 2*x |
/ 2 *atan|——————|
2 /
——————————
2
$$frac{sqrt{2}}{2} {atan}{left (frac{sqrt{2}}{2} sqrt{2 x – 1} right )}$$
