Evaluate the integral: $\displaystyle \int\frac{{{20}}}{{{x}^{{2}}\sqrt{{{x}^{{2}}+{81}}}}}{\left.{d}{x}\right.}$

(A) Which trig substitution is correct for this integral?


(B) Which integral do you obtain after substituting for $\displaystyle {x}$ and simplifying?
Note: to enter $\displaystyle \theta$, type the word theta.
$\displaystyle \int$ $\displaystyle {d}\theta$
Preview Question 1 Part 2 of 4  

(C) What is the value of the above integral in terms of $\displaystyle \theta$?
$\displaystyle +{C}$
Preview Question 1 Part 3 of 4  

(D) What is the value of the original integral in terms of $\displaystyle {x}$?
$\displaystyle +{C}$
Preview Question 1 Part 4 of 4