# MATA32H3 : A little guide to integration.

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###### MATA32H3 Full Course Notes

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## Document Summary

: dont forget adding an arbitrary constant c after integrating! 1/x dx = x-1 dx = ln(|x|) + c. (6/x + 6) dx = 6 1/x dx + 6 dx = 6 ln(|x|) + 6x + c. 5x dx = ex ln(5) dx = 1/ln(5) ex ln(5) + c = 5x/ln(5) + c. But wait, i thought ex dx = ex + c. That is true, but dont forget about the chain rule. Think about it backwards, using differentiation. d/dx 5x = 5x ln(5) Let u = x ln(5) du = ln(5) dx. This is another method of solving the problem above, except in the example above, c=0. It can be used for simpler situations as well: Let u = x3, 1/3 du = x2 dx. But itd be wiser to just integrate that one directly. www. notesolution. com. Let u = ln(x2), du = 2/x dx.