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∫x^4+5x^3+sin(2x) dx
So a basic rule for x functions is that 1. Add 1 to the power 2. divide by the new power. So lets do this for the 2 x terms
1/5x^5+5/4*x^4
Now lets look at the sin(2x). A general rule for ∫sin(ax)dx= -1/a(cos(ax)). So now we look at our specific example and we find that ∫sin(2x)dx=-1/2(cos(2x))
So let's put it all together now and remember to add the constant of integration. ∫x^4+5x^3+sin(2x) dx= 1/5x^5+5/4*x^4-1/2(cos(2x))+C