The general method for integrating 1/(x^2 - 2x + 4) involves using the technique of partial fractions. This means breaking the original fraction into smaller, simpler fractions that can be integrated separately.
The first step is to factor the denominator, which in this case is (x^2 - 2x + 4). This can be done by completing the square or using the quadratic formula to find the roots of the polynomial.
The constants can be found by equating the coefficients of the original fraction and the partial fractions. This involves setting up a system of equations and solving for the unknown constants.
There are three possible cases when integrating 1/(x^2 - 2x + 4): when the denominator has two real and distinct roots, when it has two equal real roots, and when it has two complex roots. Each case requires a different approach to the partial fraction decomposition.
After finding the partial fraction decomposition, the integral can be simplified by using the power rule for integration and substituting back the original variables. This will result in an expression that can be easily evaluated.