integration

yes 16

\int_{1}^{16}{tan^{-1}\sqrt{\sqrt{x}-1}}dx

Put x=sec⁴@
dx=4sec⁴@tan@d@

₁¹⁶∫4@sec⁴@tan@d@------------------------------(1)

Now use integration by parts

for that u need u know ∫sec⁴@tan@d@
put tan@=p and sec²@d@=dp

∫p(1+p²)dp

=p²/2+p⁴/4

=tan²@/2+ tan⁴@/4

and using by parts in we get (1)

₁¹⁶∫4@(tan²@/2+ tan⁴@/4) - ₁¹⁶∫4(tan²@/2+ tan⁴@/4)

in the 1st part put the limits
and for the 2nd part
use tan@=t and sec²@d@=dt and solve it as we have done it earlier
put the requisite limits to get ur answer