Question

Tìm nguyên hàm các hàm số hữu tỉ sau :

a) \(\int\frac{2\left(x+1\right)}{x^2_{ }+2x-3}dx\)

b)\(\int\frac{2\left(x-2\right)dx}{x^2-4x+4}\)

Answer 1

a)

\(\int\frac{2\left(x_{ }+1\right)}{x^2+2x_{ }-3}dx=\int\frac{2x+2}{x^2+2x-3}dx\)

\(=\int\frac{d\left(x^2+2x-3\right)}{x^2+2x-3}=ln\left|x^2+2x-3\right|+C\)

Answer 2

b)\(\int\frac{2\left(x-2\right)dx}{x^2-4x+3}=\int\frac{2x-4dx}{x^2-4x+3}=\int\frac{d\left(x^2-4x+3\right)}{x^2-4x+3}=ln\left|x^2-4x+3\right|+C\)