Giải thích các bước giải:
$I=\int\dfrac{\ln^2x+1}{x}dx$
$\rightarrow I=\int(\ln^2x+1)\dfrac{1}{x}dx$
$\rightarrow I=\int \ln^2x+1d(\ln x)$
$\rightarrow I=\dfrac{1}{3}\ln^3x+\ln x+C$
$I=\int\dfrac{\sin 2x}{1+4\sin x}dx$
$\rightarrow I=\int\dfrac{2\sin x\cos x}{1+4\sin x}dx$
$\rightarrow I=\int\dfrac{2\sin x}{1+4\sin x}d(\sin x)$
$\rightarrow I=\int\dfrac{2\sin x+\dfrac{1}{2}-\dfrac{1}{2}}{1+4\sin x}d(\sin x)$
$\rightarrow I=\int\dfrac{\dfrac{1}{2}(1+4\sin x)-\dfrac{1}{2}}{1+4\sin x}d(\sin x)$
$\rightarrow I=\int \dfrac{1}{2}-\dfrac{1}{8}.\dfrac{4}{1+4\sin x}d(\sin x)$
$\rightarrow I= \dfrac{\sin x}{2}-\dfrac{1}{8}.\ln (1+4\sin x)+C$
