Giải thích các bước giải:
$\int 1+\dfrac{\tan^2x}2dx$
$=\int \dfrac{1}{2}+\dfrac{\tan^2x+1}2dx$
$=\int \dfrac{1}{2}+\dfrac{\dfrac{\sin^2x}{\cos^2x}+1}2dx$
$=\int \dfrac{1}{2}+\dfrac{\dfrac{\sin^2x+\cos^2x}{\cos^2x}}2dx$
$=\int \dfrac{1}{2}+\dfrac{\dfrac{1}{\cos^2x}}2dx$
$=\int \dfrac{1}{2}+\dfrac{1}{2\cos^2x}dx$
$=\dfrac{1}{2}x+\dfrac{1}{2}\tan x+C$
