Integration Methods Worksheet

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