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Chapter 5: Q 4 8. (page 429)

Solve the integral:鈭�xlnxdx

Short Answer

Expert verified

The required answer isx24ln(x)-x28+c.

Step by step solution

01

Step 1. Given information. 

We have given integral is鈭�xlnxdx.

02

Step 2. Solve the integration by parts .  

We have,

鈭�xlnxdx=鈭�x2lnxdx=12鈭�xlnxdx

u=lnxdu=dxx

and

dv=xdxv=鈭�xdxv=x22

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

localid="1648797136253" 12鈭�xlnxdx=12lnxx22-鈭�x221xdx=12x22lnx-12鈭�xdx=x24ln(x)-x28+c

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Most popular questions from this chapter

Why doesn鈥檛 the definite integral鈭�231-x2dx make sense? (Hint: Think about domains.)

Find three integrals in Exercises 21鈥�70 in which the denominator of the integrand is a good choice for a substitution u(x).

Solve鈭�x4+x2dxthe following two ways:

(a) with the substitution u=4+x2;

(b) with the trigonometric substitution x = 2 tan u.

Solve given definite integral.

鈭�04鈥�x3x2+4dx

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

u(x)=x2+1
See all solutions

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