Упр.991 ГДЗ Алимов 10-11 класс (Алгебра)

1) sin(2x+3);
2) cos(3x+4);
3) cos(x/2 — 1);
4) sin(x/4 + 5);
5) e^((x+1)/2);
6) e^(3x-5);
7) 1/2x;
8) 1/(3x-1).

1. $$\int \sin(2x+3)\,dx = -\frac{1}{2}\cos(2x+3)+C$$

2. $$\int \cos(3x+4)\,dx = \frac{1}{3}\sin(3x+4)+C$$

3. $$\int \cos\left(\frac{x}{2}-1\right)\,dx = 2\sin\left(\frac{x}{2}-1\right)+C$$

4. $$\int \sin\left(\frac{x}{4}+5\right)\,dx = -4\cos\left(\frac{x}{4}+5\right)+C$$

5. $$\int e^{\frac{x+1}{2}}\,dx = 2e^{\frac{x+1}{2}}+C$$

6. $$\int e^{3x-5}\,dx = \frac{1}{3}e^{3x-5}+C$$

7. $$\int \frac{1}{2x}\,dx = \frac{1}{2}\ln|x|+C$$

8. $$\int \frac{1}{3x-1}\,dx = \frac{1}{3}\ln|3x-1|+C$$

Ответ

1. $$-\frac{1}{2}\cos(2x+3)+C$$
2. $$\frac{1}{3}\sin(3x+4)+C$$
3. $$2\sin\left(\frac{x}{2}-1\right)+C$$
4. $$-4\cos\left(\frac{x}{4}+5\right)+C$$
5. $$2e^{\frac{x+1}{2}}+C$$
6. $$\frac{1}{3}e^{3x-5}+C$$
7. $$\frac{1}{2}\ln|x|+C$$
8. $$\frac{1}{3}\ln|3x-1|+C$$