[Toán 12] Tính nguyên hàm

F

flames.of.desire

a,
[tex]I = \int\limits tan^2x.tanx= \int\limits \frac{1-cos^2x}{cos^2x}.tanx= \int \limits\frac{tanx}{cos^2x}- \int\limits tanx = \int\limits\frac{tanx}{cos^2x}- ln(cosx) = J +ln(cosx)[/tex]
Ta có :[tex] J = \int\limits\frac{tanx}{cos^2x}- ln(cosx)[/tex]
Đặt u=tan x => [tex]du= \frac{1}{cos^2x}dx [/tex]
=>[tex]J = \int\limits u du= \frac{u^2}{2}[/tex]
=>[tex] I=\frac{u^2}{2} +ln(cosx)[/tex]
 
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F

flames.of.desire

b,
Đặt x= sin t \Rightarrow dx = cos t dt
[TEX]\Rightarrow I = \int\limits \sqrt{1- sin^2 t} . cos t dt = \int\limits cos^2 t dt = \int\limits \frac{cos 2t + 1}{2} dt= \frac{sin 2t}{4} + \frac{1}{2} t[/TEX]
 
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