Chapter 1.7, Problem 417E

In the following exercises, solve for the antiderivative ${\displaystyle \int f}$ of with C = 0, the given interval [a, b]. Approximate a value of C, if possible, such that adding C to the antidelivative gives the same value as the definite integral $F\left(x\right)={\displaystyle {\int }_a^{x}f\left(t\right)dt}$ .

417. [T] ${\displaystyle \int \frac{1}{x\sqrt{x^2-4}}}dx$ over [2, 6]