Chapter 12.2, Problem 41E

(a)

To determine

To calculate: The value of integral ${\displaystyle \int \frac{3dx}{{\left(2x-1\right)}^{3/5}}}$.

(b)

To determine

To graph: The family member of the solution to part (a) which passes through point $\left(0,2\right)$.

(c)

To determine

The values of x where the function $f\left(x\right)$ is not defined but $F\left(x\right)$ is if $f\left(x\right)=\frac{3}{{\left(2x-1\right)}^{3/5}}$ and $F\left(x\right)=\frac{15}{4}{\left(2x-1\right)}^{2/5}-\frac{7}{4}$.

(d)

To determine

The nature of tangent line of $F\left(x\right)$ at the point obtained in part (c) which is $x=\frac{1}{2}$.