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[TEX]\int_{0}^{\pi/4} tan^6.xdx[/TEX]
=[TEX]\int_{0}^{\pi/4}tan^4x(\frac{1}{cos^2x}-1)dx[/TEX]
[TEX]=-\int_{0}^{\frac{\pi}{4}}tan^2x(\frac{1}{cos^2x}-1)dx+\int_{0}^{\frac{\pi}{4}}tan^4xd(tanx)[/TEX]
[TEX]=(\frac{tan^5x}{5}-\frac{tan^3x}{3}+tanx-1)...[/TEX]
=[TEX]\frac{1}{5}-\frac{1}{3}=...[/TEX]
 
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