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Chapter 5: Q 46. (page 429)

Solve the integral:鈭�lnxdx

Short Answer

Expert verified

The required answer isx2lnx-x2+c.

Step by step solution

01

Step 1. Given information. 

We have given integral is鈭�lnxdx.

02

Step 2. Solve the integration by parts . 

We have,

u=lnxdu=dxx

and

role="math" dv=dxv=鈭�dxv=x

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

鈭�lnxdx=鈭�12lnxdx=12鈭�lnxdx=12lnxx-鈭�x.1xdx=12lnxx-鈭�1dx=x2lnx-x2+c

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Most popular questions from this chapter

Solve given integrals by using polynomial long division to rewrite the integrand. This is one way that you can sometimes avoid using trigonometric substitution; moreover, sometimes it works when trigonometric substitution does not apply.

鈭�x3-3x2+2x-3x2+1dx

Solve the integral:鈭�(x-ex)2dx

For each integral in Exercises 5鈥�8, write down three integrals that will have that form after a substitution of variables.

鈭�1udu

Solve the integral: 鈭�xsinx2dx.

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
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