Page 58 - Integration Problems
P. 58
1
∫
3
2
+ 6 + 11 + 6
−0.5
1
= ∫
( + 3)( + 2)( + 1)
−0.5
Express the denominator as partial fractions,
1
( + 3)( + 2)( + 1)
= + +
( + 3) ( + 2) ( + 1)
1 = ( + 2)( + 1) + ( + 3)( + 1)
+ ( + 3)( + 2)
Expand the contents of the brackets,
2
1 = ( + + 2 + 2)
2
+ ( + + 3 + 3)
2
+ ( + 2 + 3 + 6)
2
2
2
1 = ( + 3 + 2) + ( + 4 + 3) + ( +
5 + 6)
54
