[ Toán 12] Nguyên hàm

L

linkinpark_lp

Vừa học xong cái này nên mạn phép chém bừa vậy :D
1,

$\
\int {\sin 7x.c{\rm{os}}5x.dx} = \frac{1}{2}\int {\left( {\sin 12x + \sin 2x} \right).} dx
\ $

2,

$ \
\int {\left( {\tan ^6 x + \tan ^4 x} \right).dx} = \int {\tan ^4 x.\left( {\tan ^2 x + 1} \right).} dx = \int {\tan ^4 x.d\left( {{\mathop{\rm t}\nolimits} {\rm{anx}}} \right)}
\ $

3,

$ \
\int {\left( {\sin ^4 x + c{\rm{os}}^4 x} \right).dx} = \int {\left[ {\left( {\sin ^2 x + c{\rm{os}}^2 x} \right) - 2\sin ^2 x.c{\rm{os}}^2 x} \right].} dx = \int {\left( {1 - \frac{{\sin ^2 2x}}{2}} \right)} .dx
\ $
 
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