EXAMPLE 4 Evaluate (a) \\( \\int \\frac{1}{x^{2}+4 x+5} d x \\) and Solution (a) \\[ \\begin{array}{rlrl} \\int \\frac{d x}{x^{2}+4 x+5} & =\\int \\frac{d x}{(x+2)^{2}+1} \\quad \\begin{array}{l} \\text { Let } t=x+2 \\\\ \\text { Then } d t=d \\end{array} \\\\ & =\\int \\frac{d t}{t^{2}+1} & \\\\ & =\\tan ^{-1} t+C=\\tan ^{-1}(x+2)+C \\end{array} \\]