Quiz about Алғашқы функция. Анықталмаған интеграл

Question 1

$$\int_{ }^{ }\left(9x^2+\sin3x\right)dx$$

Accepted Answer

$$3x^3-\frac{1}{3}\cos3x+C$$

Answer

$$9x^3+\cos3x+C$$

Answer

$$3x^3-\frac{1}{3}\cos x+C$$

Answer

$$3x^3+\frac{1}{3}\cos3x+C$$

Question 2

$$\int_{ }^{ }\left(\frac{1}{x^2}+12x^8\right)dx$$

Accepted Answer

- $$-\frac{1}{x}+\frac{4}{3}x^9+C$$

Answer

$$\frac{1}{x}+\frac{4}{3}x^9+C$$

Answer

$$\frac{1}{x^3}+\frac{4}{3}x^9+C$$

Answer

$$\frac{2}{x^3}+\frac{4}{3}x^9+C$$

Question 3

$$\int\left(\frac{\cos2x}{\sin^2x}-7\right)+C$$

Accepted Answer

$$-\operatorname{ctg}x-2x-7x+C$$

Answer

$$-\operatorname{ctg}x-7x+C$$

Answer

$$\frac{1}{2}\sin2x-\operatorname{ctg}x-7x+C$$

Answer

$$\frac{1}{2}\sin2x-7x+C$$

Question 4

$$\int\left(4x^2+\frac{9}{x^2}\right)dx=$$

Accepted Answer

$$\frac{4}{3}x^3-\frac{9}{x}+C$$

Answer

$$\frac{4}{3}x^3+\frac{9}{x}+C$$

Answer

$$\frac{4}{3}x^3+\frac{3}{x^3}+C$$

Answer

$$8x+\frac{9}{x^3}+C$$

Question 5

$$\int\left(\frac{dx}{\sqrt[]{2x+1}}\right)=$$

Accepted Answer

$$\sqrt[]{2x+1}+C$$

Answer

$$2\ \sqrt[]{2x+1}+C$$

Answer

$$\frac{1}{2}\ \sqrt[]{2x+1}+C$$

Answer

$$\frac{2}{\sqrt[]{2x+1}}+C$$

Question 6

$$\int\left(\frac{1}{\cos^2\left(2x-\frac{\pi}{3}\right)}\right)dx=$$

Accepted Answer

$$\frac{1}{2}tg\left(2x-\frac{\pi}{3}\right)+C$$

Answer

$$tg\left(2x-\frac{\pi}{3}\right)+C$$

Answer

$$\frac{1}{2}tg2x+C$$

Answer

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