tdf

1. 1)
2
2 3 27Xsenx dx  =   3 243cos xc
V= 3 x
dv= 3 2 x dx
dx= 2 1
3
x dv
1
= 27
2 2   2  x sen v x dv
3
sen v
()
= 27
2 dv 
3
1
= 27
2   3
v dv
1
= 27
2   3
 sen v dv
1
= 27 2  cos
  3
 v
=   3 243 cos x
=   3 243cos x  c

2. 2)
  3
2 27 x
 dx
=
ex 4
=
  3
4
2 27 x
dx
e x 
=
227 1
dx
e x 
=
 
 
2 27
ln x
e
  54 ln x
e

  54 ln x
C

e

3. 3)  54cos 27 ln  x C
2 2
27 x
 
27 3
dx
e x
2
27 1
 27

dx
ex
 
2
27
27
ln x
e

 
729 ln x
27
e

 
729 ln x

27
C
e

4. 4)
3
2
x
 x sec dx 
27
3 3 3 3 3
 x    x   x     x   x
 
                  
             
2 sec 9ln sin cos 9ln cos sin
x dx C
27 54 54 54 54

5)
 
  2
2 27
27
x
sec x  =
 
  2
2 27
sec 27
x
dx
x
 
 
 
2 27 1
sec 27
dx
x
 
 
 
 
2 27
 ln
x
sec 27
 54cos27lnx
 54cos27 ln x C