Page 21 - Integration Problems

1 2
∫
2
2 1 − 2 2

Express the integral as,

1 2
∫
2 1 ( + 2)( − 2)

Express the denominator as partial fractions,

1
= +
( + 2)( − 2) + 2 − 2

1 = ( − 2) + ( + 2)

1 = − 2 + + 2

Equate coefficients,

1 = −2 + 2

0 = + , = −

1 = 2 + 2

1 1
= , = −
4 4

1 1 1
= − +
( + 2)( − 2) 4( + 2) 4( − 2)

17