Integration With Partial Fractions Examples 2

## Example 1

**Evaluate the following integral: $\int_0^1 \frac{x^3 +2x}{x^4 + 4x^2 + 3} \: dx$.**

## Example 2

**Evaluate the following integral: $\int \frac{x^2 -3x + 7}{(x^2 -4x + 6)^2} \: dx$.**

## Example 3

**Evaluate the following integral: $\int \frac{x^3}{(x^2 + 1)^{1/3}} \: dx$.**

## Example 4

**Evaluate the following integral: $\int \frac{\sqrt{x+1}}{x} \: dx$.**