Question

# Evaluate the following integral: \int \frac{x+3}{x-1}dx

Applications of integrals
Evaluate the following integral: $$\int \frac{x+3}{x-1}dx$$

$$I=\int \frac{x+3}{x-1}dx$$
$$=\int \frac{x+3-1+1}{x-1}dx$$
$$=\int \frac{x-1+4}{x-1}dx$$
$$=\int 1dx + \int \frac{4}{x-1}dx$$
$$=x+4\log |x-1|+c$$
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