Chapter 5.5, Problem 303E

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.

303. [T] ${\displaystyle \int 3x^2\sqrt{2x^3+1}dx\text{over}\left[0,1\right]}$