Let x >0 be a fixed real number. Then the integral ₀^ e^ -t |x-t| d t is equal to.

Step-by-step solution

₀^ x e ^ -t |( x - t )| dt = ₀^ x e ₁₁⁻¹( x - t ) dt + _ x ^ x e ₁₁⁻¹( t - x ) dt -( x - t ) e ^ -t -(-1) e ^ - t ₀^ x - -( x - t ) e ^ - t + e ^ -t )_ x = x +2 e ^ -x -1