# complex irrational definite integration

Finding value of $$\frac{8}{\pi}\int^{2}_{0}\frac{1}{x^2-x+1+\sqrt{x^4-4x^3+9x^2-10x+5}}$$

Let $$I=\int^{2}_{0}\frac{1}{x^2-x+1+\sqrt{x^4-4x^3+9x^2-10x+5}}dx$$

$$I=\int^{2}_{0}\frac{1}{x(x-1)+\sqrt{(x^2-2x)^2+5x(x-2)+5)}}dx$$

From $$\displaystyle \int^{a}_{0}f(x)dx=\int^{a}_{0}f(a-x)dx$$

$$I=\int^{2}_{0}\frac{1}{(2-x)(1-x)+\sqrt{(2-x)^2x^2+5(2-x)(-x)+5}}dx$$

How do i solve it help me please