📚 Textbook Problems

Question 1

Medium

$$\int \frac{3x^2}{x^6 + 1} \, dx$$

Question 2

Medium

$$\int \frac{1}{\sqrt{1 + 4x^2}} \, dx$$

Question 3

Medium

$$\int \frac{1}{\sqrt{(2-x)^2 + 1}} \, dx$$

Question 4

Medium

$$\int \frac{1}{\sqrt{9 - 25x^2}} \, dx$$

Question 5

Hard

$$\int \frac{3x}{1 + 2x^4} \, dx$$

Question 6

Hard

$$\int \frac{x^2}{1 - x^6} \, dx$$

Question 7

Medium

$$\int \frac{x-1}{\sqrt{x^2 - 1}} \, dx$$

Question 8

Hard

$$\int \frac{x^2}{\sqrt{x^6 + a^6}} \, dx$$

Question 9

Hard

$$\int \frac{\sec^2 x}{\sqrt{\tan^2 x + 4}} \, dx$$

Question 10

Medium

$$\int \frac{1}{\sqrt{x^2 + 2x + 2}} \, dx$$

Question 11

Medium

$$\int \frac{1}{9x^2 + 6x + 5} \, dx$$

Question 12

Medium

$$\int \frac{1}{\sqrt{7 - 6x - x^2}} \, dx$$

Question 13

Hard

$$\int \frac{1}{\sqrt{(x-1)(x-2)}} \, dx$$

Question 14

Medium

$$\int \frac{1}{\sqrt{8 + 3x - x^2}} \, dx$$

Question 15

Hard

$$\int \frac{1}{\sqrt{(x-a)(x-b)}} \, dx$$

Question 16

Hard

$$\int \frac{4x+1}{\sqrt{2x^2 + x - 3}} \, dx$$

Question 17

Hard

$$\int \frac{x+2}{\sqrt{x^2 - 1}} \, dx$$

Question 18

Hard

$$\int \frac{5x-2}{1 + 2x + 3x^2} \, dx$$

Question 19

Hard

$$\int \frac{6x+7}{\sqrt{(x-5)(x-4)}} \, dx$$

Question 20

Hard

$$\int \frac{x+2}{\sqrt{4x - x^2}} \, dx$$

Question 21

Hard

$$\int \frac{x+2}{\sqrt{x^2 + 2x + 3}} \, dx$$

Question 22

Hard

$$\int \frac{x+3}{x^2 - 2x - 5} \, dx$$

Question 23

Hard

$$\int \frac{5x+3}{\sqrt{x^2 + 4x + 10}} \, dx$$

Question 24 (MCQ)

MCQ

$$\int \frac{dx}{x^2 + 2x + 2}$$

Question 25 (MCQ)

MCQ

$$\int \frac{dx}{\sqrt{9x - 4x^2}}$$