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Tutorial Exercise Evaluate the indefinite integral. Vinter dx 1 + x18 Step 1 We must decide what to choose for u. If u = f(x), then du = f'(x) dx, and so it is helpful to look for some expression in x8 dx for which the derivative is also present, though perhaps missing a constant 1 + x18 factor. 17 Finding u in this integral is a little trickier than in some others. We see that 1 + x18 is part of this integral, but the derivative of 1 + x18 is , which is not present in the integrand. However, notice that the x8 in the numerator is close to the derivative of x', which is Submit Skip (you cannot come back)

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Answer 1

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Solution: Sien 1+x 18 Apply u-substitution : u = xº = 9x9-1 = 9x 1 dx = du 1 = // 1+x18 9x 1 9(1+x) = 1 9(1+wysig J adu 9 1+u 1 za arctan (u) 9 Substitute backu= x 1 arctan (3) 9 Adda constant 1 = arctan (x)+C