Question

integration of dx/(4sin²x + 5cos²x)
​

Answer 1

Answer:

22Integ.1/(4sin^2 x+ 5cos^2 x) dx

=Integ.1/{sin^2 x(4 + 5cot^2 x)} dx

= Integ. cosec^2 x/}{5(4/5 + cot^2 x)} dx

Let cot x = t. => -cosec^2 x dx = dt

=(-1/5)Integ.dt/{(2/√5)^2+t^2}

= -1/5) integ.{1/(2/√5)}tan^(-1) t/(2/√5)+c

= (-1/5)(√5/2) tan^(-1) (√5cot x)/2+c

= (-1/√5)tan^(-1) {√5 cotx/2} + c

Step-by-step explanation:

please mark as brilliant