Chapter 8.5, Problem 65E

a.

To determine

Whether the statement “To evaluate ${\displaystyle \int \frac{4x^6}{x^4+3x^2}dx}$, the first step is to find the partial fraction decomposition of the integrand” is true or false.

b.

To determine

Whether the given statement “To easiest way to evaluate ${\displaystyle \int \frac{6x+1}{3x^2+x}dx}$, the first step is to find the partial fraction decomposition of the integrand” is true or false.

c.

To determine

Whether the given statement “The rational function $f\left(x\right)=\frac{1}{x^2-13x+42}$

has an irreducible quadratic denominator” is true or false.

d.

To determine

Whether the given statement “The rational function $f\left(x\right)=\frac{1}{x^2-13x+43}$ has an irreducible quadratic denominator” is true or false.