Дано
$$frac{1}{sqrt{13}} log{left (frac{2 tan{left (x right )} – sqrt{13} + 3}{2 tan{left (x right )} + 3 + sqrt{13}} right )}$$
Подстановка условия
$$frac{1}{sqrt{13}} log{left (frac{2 tan{left (x right )} – sqrt{13} + 3}{2 tan{left (x right )} + 3 + sqrt{13}} right )}$$
log((2*tan((-4)) – sqrt(13) + 3)/(3 + sqrt(13) + 2*tan((-4))))/sqrt(13)
$$frac{1}{sqrt{13}} log{left (frac{2 tan{left ((-4) right )} – sqrt{13} + 3}{2 tan{left ((-4) right )} + 3 + sqrt{13}} right )}$$
log((2*tan(-4) – sqrt(13) + 3)/(3 + sqrt(13) + 2*tan(-4)))/sqrt(13)
$$frac{1}{sqrt{13}} log{left (frac{- sqrt{13} + 2 tan{left (-4 right )} + 3}{2 tan{left (-4 right )} + 3 + sqrt{13}} right )}$$
sqrt(13)*(pi*i + log(-(3 – sqrt(13) – 2*tan(4))/(3 + sqrt(13) – 2*tan(4))))/13
$$frac{sqrt{13}}{13} left(log{left (- frac{- sqrt{13} – 2 tan{left (4 right )} + 3}{- 2 tan{left (4 right )} + 3 + sqrt{13}} right )} + i piright)$$
Степени
$$frac{sqrt{13}}{13} log{left (frac{2 tan{left (x right )} – sqrt{13} + 3}{2 tan{left (x right )} + 3 + sqrt{13}} right )}$$
Численный ответ
0.277350098112615*log((2*tan(x) – sqrt(13) + 3)/(3 + sqrt(13) + 2*tan(x)))
Рациональный знаменатель
$$frac{sqrt{13}}{13} log{left (frac{2 tan{left (x right )} – sqrt{13} + 3}{2 tan{left (x right )} + 3 + sqrt{13}} right )}$$
Объединение рациональных выражений
$$frac{sqrt{13}}{13} log{left (frac{2 tan{left (x right )} – sqrt{13} + 3}{2 tan{left (x right )} + 3 + sqrt{13}} right )}$$
Общее упрощение
/ ____
____ |3 – / 13 + 2*tan(x)|
/ 13 *log|———————|
| ____ |
3 + / 13 + 2*tan(x)/
———————————
13
$$frac{sqrt{13}}{13} log{left (frac{2 tan{left (x right )} – sqrt{13} + 3}{2 tan{left (x right )} + 3 + sqrt{13}} right )}$$
Соберем выражение
$$frac{sqrt{13}}{13} log{left (frac{2 tan^{3}{left (x right )}}{2 tan^{3}{left (x right )} + 9 tan^{2}{left (x right )} + 3 sqrt{13} tan^{2}{left (x right )} + 9 sqrt{13} tan{left (x right )} + 33 tan{left (x right )} + 36 + 10 sqrt{13}} + frac{sqrt{13} tan^{2}{left (x right )}}{2 tan^{3}{left (x right )} + 9 tan^{2}{left (x right )} + 3 sqrt{13} tan^{2}{left (x right )} + 9 sqrt{13} tan{left (x right )} + 33 tan{left (x right )} + 36 + 10 sqrt{13}} + frac{9 tan^{2}{left (x right )}}{2 tan^{3}{left (x right )} + 9 tan^{2}{left (x right )} + 3 sqrt{13} tan^{2}{left (x right )} + 9 sqrt{13} tan{left (x right )} + 33 tan{left (x right )} + 36 + 10 sqrt{13}} + frac{7 tan{left (x right )}}{2 tan^{3}{left (x right )} + 9 tan^{2}{left (x right )} + 3 sqrt{13} tan^{2}{left (x right )} + 9 sqrt{13} tan{left (x right )} + 33 tan{left (x right )} + 36 + 10 sqrt{13}} + frac{3 sqrt{13} tan{left (x right )}}{2 tan^{3}{left (x right )} + 9 tan^{2}{left (x right )} + 3 sqrt{13} tan^{2}{left (x right )} + 9 sqrt{13} tan{left (x right )} + 33 tan{left (x right )} + 36 + 10 sqrt{13}} – frac{sqrt{13}}{2 tan^{3}{left (x right )} + 9 tan^{2}{left (x right )} + 3 sqrt{13} tan^{2}{left (x right )} + 9 sqrt{13} tan{left (x right )} + 33 tan{left (x right )} + 36 + 10 sqrt{13}} – frac{3}{2 tan^{3}{left (x right )} + 9 tan^{2}{left (x right )} + 3 sqrt{13} tan^{2}{left (x right )} + 9 sqrt{13} tan{left (x right )} + 33 tan{left (x right )} + 36 + 10 sqrt{13}} right )}$$
/ ____
____ |3 – / 13 + 2*tan(x)|
/ 13 *log|———————|
| ____ |
3 + / 13 + 2*tan(x)/
———————————
13
$$frac{sqrt{13}}{13} log{left (frac{2 tan{left (x right )} – sqrt{13} + 3}{2 tan{left (x right )} + 3 + sqrt{13}} right )}$$
/ ____
____ |2*tan(x) – / 13 + 3|
/ 13 *log|———————|
| ____ |
3 + / 13 + 2*tan(x)/
———————————
13
$$frac{sqrt{13}}{13} log{left (frac{2 tan{left (x right )} – sqrt{13} + 3}{2 tan{left (x right )} + 3 + sqrt{13}} right )}$$
Общий знаменатель
/ ____
____ | 3 / 13 2*tan(x) |
/ 13 *log|——————— – ——————— + ———————|
| ____ ____ ____ |
3 + / 13 + 2*tan(x) 3 + / 13 + 2*tan(x) 3 + / 13 + 2*tan(x)/
———————————————————————————
13
$$frac{sqrt{13}}{13} log{left (frac{2 tan{left (x right )}}{2 tan{left (x right )} + 3 + sqrt{13}} – frac{sqrt{13}}{2 tan{left (x right )} + 3 + sqrt{13}} + frac{3}{2 tan{left (x right )} + 3 + sqrt{13}} right )}$$
Тригонометрическая часть
/ ____
____ |3 – / 13 + 2*tan(x)|
/ 13 *log|———————|
| ____ |
3 + / 13 + 2*tan(x)/
———————————
13
$$frac{sqrt{13}}{13} log{left (frac{2 tan{left (x right )} – sqrt{13} + 3}{2 tan{left (x right )} + 3 + sqrt{13}} right )}$$
Комбинаторика
/ ____
____ | 3 / 13 2*tan(x) |
/ 13 *log|——————— – ——————— + ———————|
| ____ ____ ____ |
3 + / 13 + 2*tan(x) 3 + / 13 + 2*tan(x) 3 + / 13 + 2*tan(x)/
———————————————————————————
13
$$frac{sqrt{13}}{13} log{left (frac{2 tan{left (x right )}}{2 tan{left (x right )} + 3 + sqrt{13}} – frac{sqrt{13}}{2 tan{left (x right )} + 3 + sqrt{13}} + frac{3}{2 tan{left (x right )} + 3 + sqrt{13}} right )}$$
Раскрыть выражение
____ / / ____ / ____
/ 13 * – log3 + / 13 + 2*tan(x)/ + log3 – / 13 + 2*tan(x)//
——————————————————————
13
$$frac{sqrt{13}}{13} left(- log{left (2 tan{left (x right )} + 3 + sqrt{13} right )} + log{left (2 tan{left (x right )} – sqrt{13} + 3 right )}right)$$
/ ____
____ |3 – / 13 + 2*tan(x)|
/ 13 *log|———————|
| ____ |
3 + / 13 + 2*tan(x)/
———————————
13
$$frac{sqrt{13}}{13} log{left (frac{2 tan{left (x right )} – sqrt{13} + 3}{2 tan{left (x right )} + 3 + sqrt{13}} right )}$$
