INTERGRATION USING SUBTITUTION METHOD

HOW TO SOLVE THIS KIND OF QUESTION IN A SIMPLEST WAY. 




Firstly, the question is to be pronounce as "intergration of two ex multiply by open bracket ex restpower two plus 1 closed bracket rest power 50 with respect to the derivative of ex. 
         There are so many process/ ways of solving this kind of questions, but the most simplest method is by using subtitution method.
         Let u be the whole function that are inside the bracket and then we have
U = X^2 + 1  

du/dx = 2x

Make dx to be the subject of the formulae, we will have

dx = du/2x

Subtitute them in the original question, we will have:

  The integral of 2x ( u ) du/2x

Then we have : 2x in the numerator functions and 2x in the denominator functions, so they will cancelled each other.

Then we will have :
  
    The integral of u power 50 dx 
So, integral of udu = u power 50+1 divide by 50+1 then + the constant c
             = U power 51 divide by 51 + c
But U = X power 2  + 1, so replace it.
Then we have :

( X^2 +1 ) power 51 divide by 51 + c












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