[ tex]\int\limits_{1}^{2}f(2x^3+1/(x^2+x+1))dx[/tex]
Cả con luong giác nưa
cosx+cos^2x+sin^3x=2
[TEX]\Leftrightarrow cosx+1-sin^2x+sin^3x=2[/TEX]
[TEX]\Leftrightarrow cosx+sin^2x(sinx-1)=1[/TEX]
[TEX]\Leftrightarrow (1-cos^2x)(sinx-1)=1-cosx[/TEX]
[TEX]\Leftrightarrow \left[\begin{1-cosx=0}\\{(1+cosx)(sinx-1)=1}[/TEX]
[TEX]\Leftrightarrow sinx-1+cosxsinx-cosx=1[/TEX]
[TEX]\Leftrightarrow sinx-cosx+sinxcosx-2=0[/TEX]
đặt [TEX]t=sinx+cosx \Rightarrow sinxcosx=\frac{t^2-1}{2}[/TEX]
có [TEX]\frac{2x^3+1}{x^2+x+1}=2x-2+\frac{3}{x^2+x+1}[/TEX]
[TEX]\Rightarrow I=2\int_{1}^{2}xdx-2\int_{1}^{2}dx+\int_{1}^{2}\frac{3}{(x+\frac{1}{2})^2+\frac{3}{4}}dx[/TEX]
đặt [TEX]x+\frac{1}{2}=\frac{\sqrt[]{3}}{2}tant[/TEX] [TEX]t[/TEX] thuộc [TEX](\frac{-\pi}{2};\frac{\pi}{2})[/TEX]