Задание
Выполни задание
Таблица некоторых первообразных
| Функция \(f(x)\) | Первообразная \(F(x)\) |
| \(C\) | \(Cx+C\) |
| \(x^n, n\ne -1\) | \(\cfrac{x^{n+1}}{n+1}+C\) |
| \(\cfrac{1}{x}\) | \(\ln |x|+C\) |
| \(\cfrac{1}{\sqrt{x}}\) | \(2\sqrt{x}+C\) |
| \(\sin x\) | \(-\cos x+C\) |
| \(\cos x\) | \(\sin x+C\) |
| \(\cfrac{1}{\cos ^2x}\) | \(\tg x+C\) |
| \(\cfrac{1}{\sin ^2x}\) | \(-ctg x+C\) |
| \(e^x\) | \(e^x+C\) |
| \(a^x, a\gt0, a\ne 1\) | \(\cfrac{a^x}{\ln a}+C\) |
По таблице первообразных найди общий вид первообразных функции
| Функция \(f(x)\) | Первообразная \(F(x)\) |
| \(15\) | [ ] |
| \(x^5\) | [ ] |
| \(\sin x+2x\) | [ ] |
| \(27x^2+\cos x\) | [ ] |
| \(\cfrac{31}{\sin ^2x}\) | [ ] |