Chapter 5.2, Problem 1C

(a)

To determine

Whether the statement, “ If $u=x^2+1$ , then $du=2x$ ” is true or false.”

(b)

To determine

Whether the statement, “ If $dv=x^{2}dx$ , then $v=\frac{1}{3}{x}^3$ ” is true or false.”

(c)

To determine

Whether the statement, “ We can apply integration by parts with $u=\ln x$ and $dv=xdx$ to the integral ${\displaystyle \int \frac{\ln x}{x}dx}$ .” is true or false.

(d)

To determine

Whether the statement, “ We can apply integration by parts with $u=x$ and $dv=\ln xdx$ to the integral ${\displaystyle \int \frac{\ln x}{x}dx}$ .” is true or false.

(e)

To determine

Whether the statement, “Integration by parts has to do with reversing the product rule.”

(f)

To determine

Whether the statement, “Integration by parts is good method for any integral that involves a product.”

(g)

To determine

Whether the statement, “ In applying integration by parts, it is sometimes a good idea to choose u to be the entire integrand and let $dv=dx$ ”

(h)

To determine

Whether the statement, “ ${\displaystyle {\int }_0^{3}x{e}^{x}dx}=x{e}^x-{\displaystyle {\int }_0^3{e}^{x}dx}$ ” is true or false.