Evaluate the indefinite integral. (Use C for the constant of integration.) * V 3 - x 2 dx Tutorial Exercise Evaluate the indefinite integral. ex viot ex dx 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 ev 10 + ex dx for which the derivative is also present. We see that 10 + ex is part of this integral, and the derivative of 10 + ex is et ex . which is also present. Step 2 If we choose u = 10 + e, then du = el dx. If u = 10 + ex is substituted into e v 10 + ex ax, then we have ( = vio tex ox - fe vuex - / vuledx ) We must also convert ed dx into an expression involving u, but we already know that el dx = 1 Step 3 Now, if u = 10 + ex, then ev 10 + ex dx = / Vudu= / 43/2 du. This evaluates as 41/2 du = u (= ) 2 14 3/2 + C . 3 Step 4 Since u = 10 + ex, then converting back to an expression in x we get 2 43/2 + C = Submit Skip_(you cannot come back). Tutorial Exercise Find the general indefinite integral. 2V ( v 2 + 7 ) 2 dv Step 1 We'll begin by expanding (v2 + 7)2 - 4 + 14 2 14 v2 + 149 49 Step 2 Therefore, 2v(v2 + 7)2 = 21 5 5 + 28 28 2 3 + 98 7 98 v. Step 3 An antiderivative of 2v5 + 28v3 + 98v is 28V Submit Skip_ (you cannot come back) Tutorial Exercise Evaluate the integral . 6 x ( Six + AV/x ) dx Part 1 of 3 To find an antiderivative of f(x) = x(5V/x + 41/x). we'll first convert the radicals to fractional powers and then distribute the x. (x) = 1 5x 1/3 0 2 1/3 + 4x 174 4 2 1/4 5X 473 2 4/3 + 4x 15/4 2 5/4 Part 2 of 3 An antiderivative of f(x) = 5x4/3 + 4x5/4 is F(x) = 15/7 2 15/7 * 7/3 + 16 / 9 * * 16/ 9 * 3 / 4 2 9/4 Part 3 of 3 Now , " 5x413 + 4X5/4 dx - [45 x 713 + 15 x 3/4]1 = F(1) - F(0) Submit Skip (you cannot come back)