Algebra

# Partial Fractions - Application to Integration

Evaluate $\int_6^{18}\frac{6x^2}{x^3+15x^2+72x+108}dx.$

What is $\int\frac{1}{x^2+7x+6}dx?$

Suppose that $f(x)$ is a function whose derivative is $f'(x)=\frac{1}{x^2-2x}$ and that $f(-2)=\frac{1}{2}\ln2.$ What is the value of $f(8)?$

What is $\int\frac{x+6}{x^2-9x+20}dx?$

What is $\int\frac{1}{x^2-16}dx?$

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