(\integral\_{}^{}\frac{\sin 2x}{\sin^{4}x + \cos^{4}x}) dx =... | MATH - FUNDAMENTAL INTEGRATION | SolveeIt

$\int_{}^{}\frac{\sin 2x}{\sin^{4}x + \cos^{4}x}$ dx =

cot^–1(tan²x) + c

tan^–1(tan²x) +c

cot^–1(cot²x) + c

tan^–1 (cot²x) + cq

Answer

tan^–1(tan²x) +c

Explanation

$\int \frac { 2 \sin x \cos x } { \sin ^ { 4 } x + \cos ^ { 4 } x }$ dx = $\int \frac { 2 \tan x \sec ^ { 2 } x } { 1 + \tan ^ { 4 } x }$ dx

Put tan²x = t ̃ 2tanx. sec²x dx = dt

\ = tan^–1(t) + c = tan^–1(tan²x) + c

Question: \(\int_{}^{}\frac{\sin 2x}{\sin^{4}x + \cos^{4}x}\) dx =...