1 dx Step 1 The given improper integral is If f is continuous on the interval [0, Therefore, dx = lim ex 818 Step 2 Simplify the right side of the expression. dx. The given improper integral converges if the limit exists, otherwise it diver 1), then INFINITY S f(x) dx = lim = lim f(x) dx b3x 1 dx. e7x+ e-7x 7.x b 7x 1 lim dx = lim dx b+ Jo ex + ex b-0 0 (7x)2 +1 14x Step 3 Apply the Arctangent Rule for Integration on the right side of the expression. 7x 11