May 22, 2021

Chapters

- Exercise 1
- Exercise 2
- Exercise 3
- Exercise 4
- Exercise 5
- Exercise 6
- Exercise 7
- Exercise 8
- Exercise 9
- Exercise 10
- Exercise 11
- Solution of exercise 1
- Solution of exercise 2
- Solution of exercise 3
- Solution of exercise 4
- Solution of exercise 5
- Solution of exercise 6
- Solution of exercise 7
- Solution of exercise 8
- Solution of exercise 9
- Solution of exercise 10
- Solution of exercise 11

Calculate the following integrals:

## Exercise 1

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## Exercise 2

## Exercise 3

## Exercise 4

## Exercise 5

## Exercise 6

## Exercise 7

## Exercise 8

## Exercise 9

## Exercise 10

## Exercise 11

## Solution of exercise 1

## Solution of exercise 2

## Solution of exercise 3

If , then .

If , then

Suppose , then

If , then

If u = 6x + 10, then u' = 6

If v' = , then

## Solution of exercise 4

If u = lnx, then

If v' = 1, then v = x

## Solution of exercise 5

If , then

If v' = cos x, then v = sin x

If , then

If v' = sin x, then v = -cos x

## Solution of exercise 6

To calculate A, B and C, we substitute x with −3:

Derive and replace with −3:

x = -3 -20 = B

Derive again:

6 = 2A A = 3

Also, the coefficients can be found by realizing the operations and equaling coefficients:

-2 = 19 + B

5 = 27 + C

3 = A

B = -20

C = 38

## Solution of exercise 7

## Solution of exercise 8

t = -1 1 = -2A A =

t = 1 1 = 2B B =

## Solution of exercise 9

## Solution of exercise 10

=

## Solution of exercise 11

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