Solution The order of x2 e2x satisfies “LIATE” dv Let u = x2 dx  e2x du dx = 2x v = dx ∫e2x e 2x 2 the formula dv du x e2x 2 - 2 we have 2 2x e2x 2xdx 2 1 2 2x 2 Now we must integrate e2x dx ∫x dv let u = x dx = e2x du =1 e dx   v 2x 2 dx e 37 Using the formula dv dx u du dx dx  dx uv v 1 2 2x 2 1 1 1 2 4
Solution The order of x2 e2x satisfies “LIATE” Let u = x2 dv dx  e2x du dx = 2x v = ∫e2x dx e 2x 2 the formula dv du we have 2 2x x 2 e2x 2 - e2x 2 2xdx 1 2 2x 2 Now we must integrate ∫x e2x dx let u = x dv dx = e2x du dx =1 v  e 2x dx  2 e 37 Using the formula u dv dx dx  uv v du dx dx 2x 1 2 1 2 1 1 2 4
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