g) $G =\displaystyle\int\dfrac{\ln^2x}{x}dx$
Đặt $u =\ln x$
$\to du =\dfrac1xdx$
Ta được:
$G= \displaystyle\int u^2du$
$\to G =\dfrac{u^3}{3} + C$
$\to G =\dfrac{\ln^3x}{3} + C$
h) $H = \displaystyle\int\cos^3x\sin xdx$
Đặt $u =\cos x$
$\to du = -\sin xdx$
Ta được:
$H = -\displaystyle\int u^3du$
$\to H = -\dfrac{u^4}{4} + C$
$\to H = -\dfrac{\cos^4x}{4} + C$
i) $I = \displaystyle\int\dfrac{\tan x}{\cos^2x}dx$
Đặt $u =\tan x$
$\to du =\dfrac{1}{\cos^2x}dx$
Ta được:
$I = \displaystyle\int udu$
$\to I =\dfrac{u^2}{2} + C$
$\to I =\dfrac{\tan^2x}{2} + C$
$\left(I = \dfrac{1}{2\cos^2x} + C\right)$
