Integrate (12x^5 - 8x^3 + 3)dx giving the terms of the answer in the simplest terms

Integration is essentially differentiation in reverse! So in the simpler cases instead of multiplying by the power of x and subtracting one from the power of x, you add one to the power of x and divide by the new power. An easy way to check if you have any doubts is to differentiate your answer, especially since most people seem to get on better with differentiation!For the first term (12x^5), the integral is 2x^6, since you add one to the power of x, making 6, and then divide the coefficient by 6.The second term is converted from -8x^3 to -2x^4. Remember to treat the addition/subtraction signs as part of the whole term so you don't get confused and accidentally miss oneThe third term should be treated as 3x^0, as this makes it a bit easier to think about. The integral of this would be 3xSo the overall answer is (2x^6 - 2x^4 + 3x +c)(Remember to add +c at the end, it's easy to forget!)