The integral integration(e^(3loge^2x+5e^(2loge2x))e^(4loge^x+5e^(3loge^x-7e^{2logex})))dx, x>0 is equal to

Question

The integral \(\int\frac{e^{3log_e{2x}+5e^{2log_e2x}}}{e^{4log_ex+5e^{3log_ex}-7e^{2log_ex}}}dx, x>0,\) is equal to :

(where c is a constant of integration)

(1) log_e|x² +5x - 7| + c

(2) 4log_e|x²+ 5x- 7| + c

(3) (1/4) log_e|x² + 5x - 7| + c

(4) log_e√(x² +5x -7) + c

Answer 1

Correct option is 2