Page 39 - apuntes-cc3a1lculo-integral-2023-1

Cálculo Integral 2023-2 Ingeniería Química

ln x ln x 1  c

 x 3 dx   2x 4x
2
2

Integrar:  x arc tgxdx
1
u  arc tgx --------------- > du 1 ------------------- > du  dx

2
2
dx 1 x 1 x
x 2

dv  x ------------------ > dv  x ----------------- > v  2


2
x 2 x 1

 arc tgx xdx  arc tgx. 2   . 2 2 dx
2 1 x
2
arc tgx xdx  arc tgx. x  1 x dx


 x 2 2 1 x
2
2
1 
1 
 arc tgx xdx  arc tgx.  1 2  dx
2 2  1 x 
x 2 1   
arc tgx xdx  arc tgx.   1dx  1 
 2 2   1 x 2 
  dx

 
x 2 1
 arc tgx xdx  arc tgx.  x  arctgx  c
2 2

1 2 1 1
 arc tgx xdx  x arc tgx  x  arctgx  c
2
2
2

2

Integrar: ln x dx
du 1 1
2
u  ln x --------------------- >  2 ------------------- > du  2dx
dx x x
dv  dx > dv  x > v  x


1
 ln x dx  ln x .x  x. 2dx
2
2

x

39
Julio Meléndez Pulido