Let 2x-5=t, then x = (t+5)/2 and dx = 0.5dt

The original formula = ∫ et0.5dt = 0.5 ∫ etdt = 0.5et+c = 0.5e (2x-5).

2.

Let t = x, t = x 2, dt = 2xdx.

The original formula = ∫ e x/x2xdx = 2 ∫ e xdx = 2ex+c = 2e (√ t)+c.

3.

Let 2+2+2√x = t>；; 0,x=t^2/4-t+ 1,dx=(0.5t- 1)dt

The original formula = ∫ (0.5t-1)/TDT = ∫ (0.5-1/t) dt = 0.5t-LNT+C.

= 1+√x-ln(2+2√x)+C

Use the substitution method first, and then switch back!