общий вид первообразной для функции f(x)=1+tg^2*4x

общий вид первообразной для функции f(x)=1+tg^2*4x
- Предмет:
  Алгебра
- Автор:
  timothy7xk9
- 5 лет назад

Ответы 1

Преобразуем исходное выражение: $f(x)=1+tg^{2}4x=1+ \frac{sin^{2}4x}{cos^{2}4x} =1+ \frac{1-cos^{2}4x}{cos^{2}4x} =1+ \frac{1}{cos^{2}4x} -1=\frac{1}{cos^{2}4x}$ А теперь ищем первообразную: $\int\limits {(1+tg^{2}4x)} \, dx =\int\limits {\frac{1}{cos^{2}4x}} \, dx = \frac{1}{4} \int\limits {\frac{1}{cos^{2}4x}} \, d(4x)= \frac{1}{4} tg(4x)+C$ $\frac{1}{4}d(4x)=dx$
- Автор:
  adancontreras
- 5 лет назад
- 0
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общий вид первообразной для функции f(x)=1+tg^2*4x

Ответы 1

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