Integration using partial fractions Quiz

1. What is the form of the partial fractions of $\frac{1}{(x-2)(x^2+5)}$?

• A. $\frac{A}{x-2}+\frac{B}{x^2+5}$
• B. $\frac{A}{x-2}+\frac{B}{x+\sqrt5}+\frac{C}{x-\sqrt5}$
• C. $\frac{A}{x-2}+\frac{Bx+C}{x^2+5}$
• D. $\frac{Ax+B}{x-2}+\frac{C}{x^2+5}$

2. Find $\int\frac{2x}{x^2+7}\,dx$.

• A. $\ln(x^2+7)+c$
• B. $\arctan\frac{x}{\sqrt7}+c$
• C. $2\ln(x^2+7)+c$
• D. $\frac{2}{\sqrt7}\arctan\frac{x}{\sqrt7}+c$

3. Find $\int_0^2\frac{3}{x^2+4}\,dx$.

• A. $\frac{3\pi}{4}$
• B. $\frac{\pi}{4}$
• C. $\frac{3}{4}\ln 2$
• D. $\frac{3\pi}{8}$

4. For $\frac{9}{(x-1)(x^2+8)}=\frac{A}{x-1}+\frac{Bx+C}{x^2+8}$, find $A$.

• A. $9$
• B. $1$
• C. $\frac19$
• D. $3$

5. Find $\int\frac{1}{4x^2+25}\,dx$.

• A. $\frac14\arctan\frac x5+c$
• B. $\frac{1}{5}\arctan\frac{2x}{5}+c$
• C. $\frac{1}{10}\arctan\frac{2x}{5}+c$
• D. $\frac18\ln(4x^2+25)+c$