Use algebra to rewrite the integrand; then integrate and simplify.

Question

Use algebra to rewrite the integrand; then integrate and simplify. ​  ​

Quizplus · Accepted Answer

Rewrite the integrand using algebra:

$$\frac{x + 2}{(x - 1)^2} = \frac{x - 1}{(x - 1)^2} + \frac{3}{(x - 1)^2} = \frac{1}{x - 1} + \frac{3}{(x - 1)^2}$$

Integrate using the power rule:

$$\int \frac{x + 2}{(x - 1)^2} dx = \int \left(\frac{1}{x - 1} + \frac{3}{(x - 1)^2}\right) dx = \ln|x - 1| - \frac{3}{x - 1} + C$$

where C is the constant of integration.

Therefore, the correct answer is B.

Use Algebra to Rewrite the Integrand; Then Integrate and Simplify