i need help with my calculus homewrok

Problem 1
  21 x
dx

We know that
 








 xa
xa
Ln
aax
dx
2
1
22

  21 x
dx
=  

12x
dx

=  

12x
dx










x
x
Ln
1
1
2
1
1
1
1
2
1










x
x
Ln









x
x
Ln
1
1
2
1

    xLnxLn  11
2
1

Hence
  21 x
dx
    xLnxLn  11
2
1
Problem 3
  822 xx
dx
=   8242 xxx
dx

=
     424 xxx
dx

=
   
dx
xx 








 46
1
26
1

=  )4()2(
6
1
 xLnxLn
Therefore,
  822 xx
dx
=  )4()2(
6
1
 xLnxLn
Problem 5
  232 xx
xdx
=   222 xxx
xdx

=
   ...