Integrate 3x^2+cos(x) with respect to x

First split the question into two integrals, the integral of 3x^2 and the integral of cos(x).We'll tackle the first integral first, you have to think what value would differentiate to give 3x^2. We can see that the x part of this would be x^3 as this differentiates to 3x^2. This works out well as this has given us our answer however if this question had been to integrate 2x^2 we would have had to have multiplied the answer by 2/3 as 2/3*x^3 differentiated gives 2x^2.So the answer for the first part of the question is x^3+b (as we must never forget the constant of integration).Then we tackle the second part (integrate cos(x) with respect to x). We know that sin(x) differentiates to cos(x) so the answer for this part is simply sin(x)+d (a different constant of integration).We then just add the answers: x^3+b+sin(x)+d.As b and d are both unknown constants of integration we can just add these to give one constant of integration (c).So the answer is: x^3+sin(x)+c