Chapter 5.5, Problem 301E

In the following exercises, evaluate the indefinite integral ${\displaystyle \int f\left(x\right)dx}$ with constant C = 0 using u-substitution.

Then, graph the function and the antiderivative over the indicated interval. If possible, estimate a value of C that would need to be added to the antiderivative to make it equal to the definite integral $F\left(x\right)={\displaystyle {\int }_a^{x}f\left(t\right)dt}$ with a the left endpoint of the given interval.

301. [T] ${\displaystyle \int \frac{\sin x}{{\cos }^{3}x}dx\text{over}\left[-\frac{\pi }{3},\frac{\pi }{3}\right]}$