Integration Methods Worksheet

Solutions

Calculate the following integrals:

1 Trigonometric Integral

2 Logarithmic Integral

3 Exponential Integral

4 Logarithmic Integral

5 Trigonometric and Exponential Integral

6 Integral

7 Integral

8 Integral

9 Integral

10 Integral

11 Trigonometric Integral

12 Integral


1

Integral Exercise

Derive

Integrate

integral

Integral Solution


2

Integral Exercise

Derive

Integrate

Integral Solution


3

Integral Exercise

Derive

Integrate

Integral Operations

Derive

Integrate

Integral Operations

Derive

Integrate

Integral Operations

Integral Operations

Integral Solution


4

Integral Exercise

Derive

Integrate

Integral Operations

Integral Solution


5

Integral Exercise

Derive

Integrate

Integral Operations

Derive

Integrate

Integral Operations

Integral Operations

Integral Solution


6

Integral Exercise

Integral Operations

Integral Operations

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

Derive and replace with −3:

Integral Operations

Integral Operations

Derive again:

Integral Operations

Integral Operations

Integral Solution


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

Integral Operations

Integral Solution


7

Integral Exercise

Change of Variable

Integral Operations

Integral Operations

Integral Operations

Integral Operations

Integral Solution


8

Integral Exercise

Change of Variable

Integral Operations

Integral Operations

Integral Operations

Integral Operations

Integral Operations

Integral Operations

Change of Variable

Integral Solution


9

Integral Exercise

Change of Variable

Integral Operations

Integral Operations

Integral Operations

Integral Operations

Integral Solution


10

Integral Exercise

Change of Variable

Integral Operations

Integral Operations

Integral Operations

Integral Operations

Integral Operations

Integral Solution


11

Integral Exercise

Integral Operations

Integral Operations

Integral Operations

Integral Operations

Integral Solution


12

Integral Exercise

Change of Variable

Integral Operations

Integral Operations

Integral Solution