Integrals Yielding Natural Log Function with Audio, Lecture notes of Engineering Mathematics

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INTEGRALS YIELDING THE

NATURAL LOGARITHMIC

FUNCTION

u

du

Re call : d ln u 

ln u  C  u du

EXAMPLE: 

dx

x x 5

4x 2

2

EXAMPLE: 

dx

x ln x

Practice: Evaluate the following integral. 2 4 3 dx x   (^)  dy y ln y

  ds 3 s 2 2 s 3

dt t sin t 1 cos t 

dx

xln x

  

3 2 dx x 4 x x 2 1 0 2 1 2 2 x dx x x   

1 / 3 dw 3 w 2 2 w 3 4 3 5 4 3 12 6 5 16 12 x x dx x x x       ^

 1 0 2 1 d ( 1 ) Tan

   dx x 1 x 3 x 2 3

 

1 2 2 3 dt t t t t