Integrals Yielding the Natural Logarithmic Function: A Comprehensive Guide with Exercises, Slides of Differential and Integral Calculus

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INTEGRALS

YIELDING THE

NATURAL

LOGARITHMIC

FUNCTION

INTEGRALS YIELDING THE NATURAL

LOGARITHMIC FUNCTION

• (^) Define the natural logarithmic function;
• (^) Illustrate solutions on problem yielding to

natural

logarithmic function;

• Derive particular formulas involving

integrals relative

to natural logarithmic function; and

• (^) evaluate problems involving natural

logarithmic

OBJECTIVES:

dx

2x- 7



EXAMPLE:



dx

x x 5

4x 2

2   3 0 4 3 dx x 1 x 3. 

dx

4 - x

x 3x

3

EXERCISES: Evaluate the following integral.

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

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