Problem : Compute dx .
The denominator x ^{2} - 3x + 2 factors as (x - 1)(x - 2) . We set
+ = , |
5x - 7 | = | A(x - 2) + B(x - 1) | |
= | (A + B)x + (- 2A - B) |
A + B | = | 5 | |
-2A - B | = | -7 |
dx | = | dx + dx | |
= | 2 log(x - 1) + 3 log(x - 2) + C |
Problem : Compute dx using change of variables and partial fraction decomposition.
Letting u = e ^{x} , we have
du | = | du + du | |
= | 2 log(u - 4) + log(u + 2) + C | ||
= | 2 log(e ^{x} -4) + log(e ^{x} + 2) + C |