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Integrals of Simple Functions

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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


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


Example 3: Evaluate ∫15678dx


∫15678dx  = 15678x+C

Example 4: Evaluate ∫6x2 + 4dx



      ∫6x2 + 4dx


= 6∫x2dx + 4∫dx


=6x3/3 + 4x + C


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