Дано
$$frac{1}{2 sqrt{13}} left(-1 log{left (frac{6 t – 2 sqrt{13} – 4}{6 t + -4 + 2 sqrt{13}} right )}right)$$
Подстановка условия
$$frac{1}{2 sqrt{13}} left(-1 log{left (frac{6 t – 2 sqrt{13} – 4}{6 t + -4 + 2 sqrt{13}} right )}right)$$
(-log((6*(-3) – 2*sqrt(13) – 4)/(-4 + 2*sqrt(13) + 6*(-3))))/(2*sqrt(13))
$$frac{1}{2 sqrt{13}} left(-1 log{left (frac{6 (-3) – 2 sqrt{13} – 4}{6 (-3) + -4 + 2 sqrt{13}} right )}right)$$
(-log((6*(-3) – 2*sqrt(13) – 4)/(-4 + 2*sqrt(13) + 6*(-3))))/(2*sqrt(13))
$$frac{1}{2 sqrt{13}} left(-1 log{left (frac{-3 cdot 6 – 2 sqrt{13} – 4}{-3 cdot 6 + -4 + 2 sqrt{13}} right )}right)$$
-sqrt(13)*log((-22 – 2*sqrt(13))/(-22 + 2*sqrt(13)))/26
$$- frac{sqrt{13}}{26} log{left (frac{-22 – 2 sqrt{13}}{-22 + 2 sqrt{13}} right )}$$
Степени
$$- frac{sqrt{13}}{26} log{left (frac{6 t – 2 sqrt{13} – 4}{6 t – 4 + 2 sqrt{13}} right )}$$
Численный ответ
-0.138675049056307*log((6*t – 2*sqrt(13) – 4)/(-4 + 2*sqrt(13) + 6*t))
Рациональный знаменатель
$$- frac{sqrt{13}}{26} log{left (- frac{- 6 t + 4 + 2 sqrt{13}}{6 t – 4 + 2 sqrt{13}} right )}$$
Объединение рациональных выражений
$$- frac{sqrt{13}}{26} log{left (frac{3 t – sqrt{13} – 2}{3 t – 2 + sqrt{13}} right )}$$
Общее упрощение
/ / ____
____ |-2 + / 13 – 3*t/ |
-/ 13 *log|——————–|
| ____ |
-2 + / 13 + 3*t /
———————————-
26
$$- frac{sqrt{13}}{26} log{left (- frac{- 3 t + 2 + sqrt{13}}{3 t – 2 + sqrt{13}} right )}$$
Соберем выражение
$$- frac{sqrt{13}}{26} log{left (frac{6 t – 2 sqrt{13} – 4}{6 t + -4 + 2 sqrt{13}} right )}$$
/ ____
____ |-2 – / 13 + 3*t|
-/ 13 *log|—————–|
| ____ |
-2 + / 13 + 3*t/
——————————-
26
$$- frac{sqrt{13}}{26} log{left (frac{3 t – sqrt{13} – 2}{3 t – 2 + sqrt{13}} right )}$$
Общий знаменатель
/ ____
____ | 2 / 13 3*t |
-/ 13 *log|- —————– – —————– + —————–|
| ____ ____ ____ |
-2 + / 13 + 3*t -2 + / 13 + 3*t -2 + / 13 + 3*t/
————————————————————————-
26
$$- frac{sqrt{13}}{26} log{left (frac{3 t}{3 t – 2 + sqrt{13}} – frac{sqrt{13}}{3 t – 2 + sqrt{13}} – frac{2}{3 t – 2 + sqrt{13}} right )}$$
Комбинаторика
/ ____
____ | 4 2*/ 13 6*t |
-/ 13 *log|- ——————- – ——————- + ——————-|
| ____ ____ ____ |
-4 + 2*/ 13 + 6*t -4 + 2*/ 13 + 6*t -4 + 2*/ 13 + 6*t/
——————————————————————————-
26
$$- frac{sqrt{13}}{26} log{left (frac{6 t}{6 t – 4 + 2 sqrt{13}} – frac{2 sqrt{13}}{6 t – 4 + 2 sqrt{13}} – frac{4}{6 t – 4 + 2 sqrt{13}} right )}$$
Раскрыть выражение
____ / / ____ / ____
/ 13 * – log -4 – 2*/ 13 + 6*t/ + log -4 + 2*/ 13 + 6*t//
————————————————————–
26
$$frac{sqrt{13}}{26} left(log{left (6 t – 4 + 2 sqrt{13} right )} – log{left (6 t – 2 sqrt{13} – 4 right )}right)$$
/ ____
____ | 6*t – 2*/ 13 – 4|
-/ 13 *log|——————-|
| ____ |
-4 + 2*/ 13 + 6*t/
———————————
26
$$- frac{sqrt{13}}{26} log{left (frac{6 t – 2 sqrt{13} – 4}{6 t + -4 + 2 sqrt{13}} right )}$$
