Question

Nu stiu cum se rezolva. Am incercat si cu integrarea prin parti, dar tot nu-mi iese. Ma ajutati, va rog?

Answer 1

$\text{Vom folosi formula:} \boxed{\dfrac{1}{\cos^2 x}=tg^2 x+1}\\\displaystyle \int \dfrac{1}{\cos^4 x}dx=\int \dfrac{1}{\cos^2 x}(tg^2 x+1)dx\\\text{Facem schimbarea de variabila } tg\ x\stackrel{not}{=} t\Rightarrow \dfrac{1}{\cos^2 x}dx=dt\\\int (t^2+1)dt =\int t^2 dt +\int 1dt=\dfrac{t^3}{3}+t +C=\dfrac{tg^3 x}{3}+tg\ x+C\\\text{Hope you understood.}$