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.