   Chapter 8.2, Problem 61E

Chapter
Section
Textbook Problem

# Integration by Parts State whether you would use integration by parts to find each integral. If so, identify what you would use for u and dv. Explain your reasoning.(a) ∫ ln x x d x (b) ∫ x ln   x   d x (c) ∫ x 2 e − 3 x d x (d) ∫ 2 x e x 2 d x (e) ∫ x x + 1 d x (f) ∫ x x 2 + 1 d x

(a)

To determine
Whether to use the method of integration by parts to evaluate the indefinite integral lnxxdx and to give the expressions for u and dv

Explanation

Consider the integral as lnxxdx

If one used the integration by parts for the expression then since the power of x is 1 and after differentiating it would become 1x2 means the power keep adding so this method would be futile to use

(b)

To determine
Whether to use the method of integration by parts to evaluate the indefinite integral xlnxdx and to give the expressions for u and dv

(c)

To determine
Whether to use the method of integration by parts to evaluate the indefinite integral x2e3xdx and to give the expressions for u and dv

(d)

To determine
Whether to use the method of integration by parts to evaluate the indefinite integral 2xex2dx and to give the expressions for u and dv. Whether to use integration by parts to evaluate integral 2xex2dx.

(e)

To determine
Whether to use the method of integration by parts to evaluate the indefinite integral xx+1dx and to give the expressions for u and dv

(f)

To determine
Whether to use the method of integration by parts to evaluate the indefinite integral xx2+1dx and to give the expressions for u and dv

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