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Integrals of Simple Functions

Function Integral
c cx + k, where c and k are constants
xn xn+1 / (n+1) + c, where c is a contant and is not equal to -1
x-1 = 1/x ln | x | + c, where c is a constant


Example 1: Integrate: ∫sin1/3x cosx dx

Solution:

We could either choose u = sin x, u = sin1/3x or u = cos x. However, only the first one of these works in this problem.

 

So we let u = sin x.

 

Finding the differential:

du = cos x dx

 

Substituting these into the integral gives:




Example 2: Evaluate

Solution:



Example 3: Evaluate ∫15678dx

Solution:

∫15678dx  = 15678x+C




Example 4: Evaluate ∫6x2 + 4dx

Solution:

 

      ∫6x2 + 4dx

 

= 6∫x2dx + 4∫dx

 

=6x3/3 + 4x + C

 

= 2x3 + 4x + C

 

 

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