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Chapter 5: Q 38. (page 429)

Solve the integral:鈭�ln3xdx

Short Answer

Expert verified

The required answer isxln3x-1+c.

Step by step solution

01

Step 1. Given information. 

We have given integral is鈭�ln3xdx.

02

Step 2. Solve the integration by parts .  

We have,

u=ln3xdu=dxx

and

dv=dxv=鈭�dxv=x

The formula of integration by parts is 鈭�udv=uv-鈭�vdu.

鈭�ln3xdx=ln3xx-鈭�1dx=xln3x-x+c=xln3x-1+c

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Most popular questions from this chapter

True/False: Determine whether each of the statements that follow is true or false. If a statement is true, explain why. If a statement is false, provide a counterexample.

(a) True or False: The substitution x = 2 sec u is a suitable choice for solving鈭�1x2鈭�4dx.

(b) True or False: The substitution x = 2 sec u is a suitable choice for solving鈭�1x2鈭�4dx.

(c) True or False: The substitution x = 2 tan u is a suitable choice for solving鈭�1x2+4dx.

(d) True or False: The substitution x = 2 sin u is a suitable choice for solving鈭�x2+4鈭�5/2dx

(e) True or False: Trigonometric substitution is a useful strategy for solving any integral that involves an expression of the form x2鈭�a2.

(f) True or False: Trigonometric substitution doesn鈥檛 solve an integral; rather, it helps you rewrite integrals as ones that are easier to solve by other methods.

(g) True or False: When using trigonometric substitution with x=asinu, we must consider the cases x>a and x<-a separately.

(h) True or False: When using trigonometric substitution with x=asecu, we must consider the cases x>a and x<-a separately.

Solve the integral:鈭�xlnxdx

Solve given definite integral.

鈭�12鈥�39鈭�2x23/2dx

Complete the square for each quadratic in Exercises 28鈥�33. Then describe the trigonometric substitution that would be appropriate if you were solving an integral that involved that quadratic.

x2鈭�4x鈭�8

For each function u(x) in Exercises 9鈥�12, write the differential du in terms of the differential dx.

u(x)=1x
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