Question

If $\int \frac{1}{(x+100)\sqrt{x+99}} dx = f(x) + c$ then $f(x) =$

• A. $2\sqrt{x+100}$
• B. $3\sqrt{x+100}$
• C. $2 \tan^{-1}\sqrt{x+99}$
• D. $2 \tan^{-1}\sqrt{x+100}$

Hint:

For integrals of the form $\frac{1}{(ax+b)\sqrt{cx+d}}$, the substitution $u = \sqrt{cx+d}$ usually leads to an arctan or log form.

Answer 1

The Correct Option is C