Let _ ^ _e 4 d x e ^x-1 = 6 . Then e ^ and e ^ - are the roots of the equation :

Step-by-step solution

aligned & _ ^ 4 dx e ^ x -1 = 6 & Let e ^ x -1= t ^2 & e ^ x dx =2 t dt & = 2 dt t ^2+1 & =2 ⁻¹ t & = .2 ⁻¹ ( e ^ x -1 ) |_ ^ _ e ^4 & =2 [ ⁻¹ 3 - ⁻¹ e ^ -1 ]= 6 & = 3 - ⁻¹ e ^ -1 = 12 & ⁻¹ e ^ -1 = 4 & e ^ =2 e ^ - = 1 2 & x ^2- (2+ 1 2 ) x +1=0 & 2 x ^2-5 x +2=0 aligned