₀^ 10 [ e^x e^x - 1 e^x + 8 ]dx =

Step-by-step solution

Let e^x - 1 = t^2 , then e^x dx = 2t dt . When x = 0 , t = 0 . When x = 10 , t = 3 . Substituting these into the integral, we get: I = ₀^3 t t^2 + 1 + 8 (2t dt) I = 2 ₀^3 t^2 t^2 + 9 dt I = 2 ₀^3 ( 1 - 9 t^2 + 9 ) dt I = 2 [ t - 3 ⁻¹ ( t 3 ) ]₀^3 I = 2 [ 3 - 3 ⁻¹(1) ] I = 2 ( 3 - 3 4 ) I = 3 2 (4 - ) Answer: 3 2 (4 - )