MCQ
$\int_0^\infty {\frac{{dx}}{{{{\left( {x + \sqrt {{x^2} + 1} } \right)}^3}}}} = $
- ✓$\frac{3}{8}$
- B$\frac{1}{8}$
- C$ - \frac{3}{8}$
- DNone of these
$\int_0^\infty {\frac{{dx}}{{{{\left( {x + \sqrt {{x^2} + 1} } \right)}^3}}}} $
$ = \int_0^{\pi /2} {\frac{{{{\sec }^2}\theta \,d\theta }}{{{{(\tan \theta + \sec \theta )}^3}}}} $
$= \int_0^{\pi /2} {\frac{{\cos \theta }}{{{{(1 + \sin \theta )}^3}}}d\theta } $
$ = \left[ { - \frac{1}{{2{{(1 + \sin \theta )}^2}}}} \right]_0^{\pi /2} $
$= - \frac{1}{8} + \frac{1}{2} = \frac{3}{8}$.
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
$(A)$ $\mathrm{S}_{\mathrm{n}}<\frac{\pi}{3 \sqrt{3}}$ $(B)$ $S_n>\frac{\pi}{3 \sqrt{3}}$
$(C)$ $T_n<\frac{\pi}{3 \sqrt{3}}$ $(D)$ $T_n>\frac{\pi}{3 \sqrt{3}}$