Question

sec²θ/tan²θ-4tanθ+3 ,Integrate the given function defined over a proper domain w.r.t. x.

Answer 1

HELLO DEAR,




GIVEN:-
∫sec²θ.dθ/tan²θ-4tanθ+3

put tanθ = t
=> sec²θ.dθ = dt

therefore,
=> I = dt/(t² - 4t + 3)

=> I = dt/(t² - 3t - t + 3)

=> I = dt/(t - 3)(t - 1)

=> I = $\bold{(-1/2)\int{\frac{(t - 3) - (t - 1)}{(t - 3)(t - 1)}}\,dt}$

=> I = (-1/2)∫dt/(t - 1) - (-1/2)∫dt/(t - 3)

=> I = -1/2log|t - 1| + 1/2log|t - 3| + C.

put the value of t = tanθ

=> I = -1/2log|tanθ - 1| + 1/2log|tanθ - 3| + C.


I HOPE ITS HELP YOU DEAR,
THANKS