intgeral of : 7^2x/7^2x-7^x+1 dx

\int \frac{7^{2 x}}{7^{2 x} - 7^{x} + 1} d x P u t 7^{x} = t T h e n 7^{x} \log 7 d x = d t t \log 7 d x = d t d x = \frac{d t}{t \log 7} T h e n \int \frac{t^{2}}{t^{2} - t + 1} \frac{d t}{t \log 7} = \frac{1}{\log 7} \int \frac{t}{t^{2} - t + 1} d t = \frac{1}{2 \log 7} \int \frac{2 t}{t^{2} - t + 1} d t (m u l t i p l y i n g a n d d i v i d i n g b y 2) = \frac{1}{2} \int \frac{2 t - 1 + 1}{t^{2} - t + 1} d t (a d d i n g a n d s u b t r a c t i n g 1) = \frac{1}{2 \log 7} \int \frac{2 t - 1}{t^{2} - t + 1} d t + \frac{1}{2 \log 7} \int \frac{1}{t^{2} - t + 1} d t (w e h a v e t^{2} - t + 1 = t^{2} - 2 * t * \frac{1}{2} + \frac{1}{4} - \frac{1}{4} + 1 = (t - \frac{1}{2})^{2} + (\frac{\sqrt{3}}{2})^{2}) = \frac{1}{2 \log 7} \log (t^{2} - t + 1) + \frac{1}{2 \log 7} \int \frac{1}{(t - \frac{1}{2})^{2} + (\frac{\sqrt{3}}{2})^{2}} = \frac{1}{2 \log 7} \log (t^{2} - t + 1) + \frac{1}{2 \log 7} \frac{1}{\frac{\sqrt{3}}{2}} \tan^{- 1} (\frac{t - \frac{1}{2}}{\frac{\sqrt{3}}{2}}) = \frac{1}{2 \log 7} \log (t^{2} - t + 1) + \frac{1}{\sqrt{3} \log 7} \tan^{- 1} (\frac{2 t - 1}{\sqrt{3}}) = \frac{1}{\log 49} \log (7^{2 x} - 7^{x} + 1) + \frac{1}{\sqrt{3} \log 7} \tan^{- 1} (\frac{2 * 7^{x} - 1}{\sqrt{3}})

intgeral of : 72x/72x-7x+1 dx