Question Number 116237 by bobhans last updated on 02/Oct/20
$$\int\:\sqrt{\mathrm{5cos}\:^{\mathrm{2}} \mathrm{x}+\mathrm{4}}\:\mathrm{dx}\:? \\ $$
Answered by Lordose last updated on 02/Oct/20
$$\int\sqrt{\mathrm{5}\left(\mathrm{1}−\mathrm{sin}^{\mathrm{2}} \mathrm{x}\right)+\mathrm{4}}\:\mathrm{dx} \\ $$$$\int\sqrt{\mathrm{9}−\mathrm{5sin}^{\mathrm{2}} \mathrm{x}}\:\mathrm{dx} \\ $$$$\mathrm{3}\int\sqrt{\mathrm{1}−\frac{\mathrm{5}}{\mathrm{9}}\mathrm{sin}^{\mathrm{2}} \mathrm{x}}\:\mathrm{dx} \\ $$$$\mathrm{3E}\left(\mathrm{x}\mid\frac{\mathrm{5}}{\mathrm{9}}\right) \\ $$$$\bigstar\boldsymbol{\mathrm{LorD}}\:\boldsymbol{\varnothing\mathrm{sE}} \\ $$
Commented by mohammad17 last updated on 02/Oct/20
$${sir}\:{what}\:{is}\:{the}\:{mean}\:{of}\:\mathrm{3}{E}\left({x}\mid\frac{\mathrm{5}}{\mathrm{9}}\right) \\ $$
Commented by mohammad17 last updated on 02/Oct/20
$${can}\:{you}\:{give}\:{me}\:{information}\:{about}\:{this} \\ $$
Answered by Bird last updated on 02/Oct/20
$${elliptic}\:{integral} \\ $$