Дано
$$frac{1}{2 sqrt{42}} log{left (frac{12 x – 2 sqrt{42}}{12 x + 2 sqrt{42}} right )}$$
Подстановка условия
$$frac{1}{2 sqrt{42}} log{left (frac{12 x – 2 sqrt{42}}{12 x + 2 sqrt{42}} right )}$$
log((12*(3/2) – 2*sqrt(42))/(2*sqrt(42) + 12*(3/2)))/(2*sqrt(42))
$$frac{1}{2 sqrt{42}} log{left (frac{12 (3/2) – 2 sqrt{42}}{12 (3/2) + 2 sqrt{42}} right )}$$
log((12*3/2 – 2*sqrt(42))/(2*sqrt(42) + 12*3/2))/(2*sqrt(42))
$$frac{1}{2 sqrt{42}} log{left (frac{- 2 sqrt{42} + frac{36}{2}}{2 sqrt{42} + frac{36}{2}} right )}$$
sqrt(42)*log((18 – 2*sqrt(42))/(18 + 2*sqrt(42)))/84
$$frac{sqrt{42}}{84} log{left (frac{- 2 sqrt{42} + 18}{2 sqrt{42} + 18} right )}$$
Степени
$$frac{sqrt{42}}{84} log{left (frac{12 x – 2 sqrt{42}}{12 x + 2 sqrt{42}} right )}$$
Численный ответ
0.077151674981046*log((12*x – 2*sqrt(42))/(2*sqrt(42) + 12*x))
Рациональный знаменатель
$$frac{sqrt{42}}{84} log{left (frac{6 x^{2} – 2 sqrt{42} x + 7}{6 x^{2} – 7} right )}$$
Объединение рациональных выражений
$$frac{sqrt{42}}{84} log{left (frac{6 x – sqrt{42}}{6 x + sqrt{42}} right )}$$
Общее упрощение
/ ____
____ |- / 42 + 6*x|
/ 42 *log|————–|
| ____ |
/ 42 + 6*x /
————————–
84
$$frac{sqrt{42}}{84} log{left (frac{6 x – sqrt{42}}{6 x + sqrt{42}} right )}$$
Соберем выражение
$$frac{sqrt{42}}{84} log{left (frac{6 x – sqrt{42}}{6 x + sqrt{42}} right )}$$
/ ____
____ |12*x – 2*/ 42 |
/ 42 *log|—————|
| ____ |
2*/ 42 + 12*x/
—————————
84
$$frac{sqrt{42}}{84} log{left (frac{12 x – 2 sqrt{42}}{12 x + 2 sqrt{42}} right )}$$
Общий знаменатель
/ ____
____ | / 42 6*x |
/ 42 *log|- ———— + ————|
| ____ ____ |
/ 42 + 6*x / 42 + 6*x/
—————————————–
84
$$frac{sqrt{42}}{84} log{left (frac{6 x}{6 x + sqrt{42}} – frac{sqrt{42}}{6 x + sqrt{42}} right )}$$
Комбинаторика
/ ____
____ | 2*/ 42 12*x |
/ 42 *log|- ————— + —————|
| ____ ____ |
2*/ 42 + 12*x 2*/ 42 + 12*x/
———————————————–
84
$$frac{sqrt{42}}{84} log{left (frac{12 x}{12 x + 2 sqrt{42}} – frac{2 sqrt{42}}{12 x + 2 sqrt{42}} right )}$$
Раскрыть выражение
____ / / ____ / ____
/ 42 * – log2*/ 42 + 12*x/ + log – 2*/ 42 + 12*x//
——————————————————–
84
$$frac{sqrt{42}}{84} left(log{left (12 x – 2 sqrt{42} right )} – log{left (12 x + 2 sqrt{42} right )}right)$$
/ ____
____ |12*x – 2*/ 42 |
/ 42 *log|—————|
| ____ |
2*/ 42 + 12*x/
—————————
84
$$frac{sqrt{42}}{84} log{left (frac{12 x – 2 sqrt{42}}{12 x + 2 sqrt{42}} right )}$$
