∫logex^2/logex^2+loge(x^2-44x+484)dx, x∈(6,16) is equal to : (1) 6 (2) 8 (3) 5 (4) 10

Question

\(\int\limits_6^{16}\frac{log_ex^2}{log_ex^2+log_e(x^2-44x+484)}dx\) is equal to :

∫log_ex²/log_ex²+log_e(x²-44x+484)dx, x∈(6,16)

(1) 6 

(2) 8 

(3) 5 

(4) 10

Answer 1

Option : (3). 5 

∫log_ex²/log_ex²+log_e(x²-44x+484)dx, x∈(6,16)

Let I = \(\int\limits_6^{16}\frac{log_ex^2}{log_ex^2+log_e(x^2-44x+484)}dx\)