Find ∫(2x^5 -4x^-3 +5) dx
So we have to integrate these 3 terms one by one. To integrate 2x5 you add 1 to the power of x, so that becomes 6, you then divide the coefficient by the new power of x. So 3/6=1/2 giving the integral of 2x5 to be 1/2 x6. Similarly, to integrate -4x-3 you add 1 to the power of x, and divide the coefficient by the new power of x giving, 2x-2. To integrate 5, you should picture it as 5x0. So following the pattern of adding one to the power and dividing the coefficient by the new power you get 5x. Finally, you need to always remember adding the integration constant (+C) . This gives the answer to be 1/2 x6 +2x-2 +5x +C.
PS
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