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: $\int \frac{\sqrt{x+1}}{x} \: dx$.