What is the primary purpose of partial fraction decomposition in calculus?

Evaluate the integral $\int \frac{1}{(x-3)(x+2)}dx$.

Evaluate the indefinite integral: $\int \frac{dx}{x(x^6+1)}$

Set up the partial fraction decomposition for $\frac{5x^2+7}{(x^2-6x+9)(x^2+2x+5)}$. Do not solve for the unknown constants.

Evaluate the integral:

${\int }_4^6\frac{4x^5+36x^3+6x^2+27}{x^3+9x}dx$