Tích phân hàm đa thức hữu tỉ?

N

nguyenbahiep1

[laTEX]\int_{0}^{1} \frac{x^4-x^2+1+x^2}{(x^2+1)(x^4-x^2+1)}dx \\ \\ \int_{0}^{1}\frac{dx}{x^2+1} + \int_{0}^{1}\frac{x^2dx}{x^6+1} \\ \\ arctanx \big|_0^1 + \frac{1}{3}\int_{0}^{1}\frac{d(x^3)}{(x^3)^2+1} \\ \\ \frac{\pi}{4} + \frac{1}{3}arctan(x^3) \big|_0^1 = \frac{\pi}{4}+\frac{\pi}{12} = \frac{\pi}{3}[/laTEX]
 
You must log in or register to reply here.
Top Bottom