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

sinudu

Short Answer

Expert verified

The three integrals 2xsinx2dx,sin(lnx)xdxand(2x+1)sin(x2+x)dxwill have form sinuduafter a substitution of variables.

Step by step solution

01

Step 1. Given Information 

For given integral we have to write down three integrals that will have that form after a substitution of variables.
sinudu

02

Step 2. The first integrals that will have that form after a substitution of variables.

Let u=x2

dudx=2xdu=2xdx

This substitution changes the integral into

localid="1648748046608" 2xsinx2dx

03

Step 3. The second integrals that will have that form after a substitution of variables.

Let

u=lnxdudx=1xdu=1xdx

This substitution changes the integral into

sin(lnx)xdx

04

Step 4. The third integrals that will have that form after a substitution of variables.

Let

u=x2+xdudx=2x+1du=(2x+1)dx

This substitution changes the integral into

(2x+1)sin(x2+x)dx

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