Question

This question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive any points for the skipped part, and you will not be able to come back to the skipped part. Tutorial Exercise Evaluate the indefinite integral. **** + 27ox 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 \x x(x3 + 2) dx for which the derivative is also present, though perhaps missing a constant factor. For example, x3 + 2 is part of this integral, and the derivative of x3 + 2 is 3x2 which 3.62 is also present except for a constant factor. Step 2 If we choose u = x3 + 2, then du = 3x2 dx. If u = x3 + 2 is substituted into x2(x3 + 2)? dx, then we have V x |xw?aa-lawan

Answer 1

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S x² x2 (2x3+2)'da t Step 2 for example 3+2 is part of this integral, and the derivative of x²+2 is 3x?', which is also except a constant factor.. Step. 2 of we choose U = 23+2 du 3x²dx of u= x²+2 is substitute into (x²(x²+2) tax then we have x² (uitda Sox (n?dx) podtWe must also conuert me? dx into an expression involving du - 30² da and so lx?dx= du

step, 3 Now then, Jut. I du I u= x3+2 fx36x² + 2) + dx = Jutdu $[4]+C ( u8] + a - 3 Iy8tc 24 put Back u= x3+2 's (21) tc Ans 24