# Calculus textbooks with good sections on integration

• Calculus
Santiago24
Hi I'm having troubles with integration specially by substitution, I'm going to read a calculus textbook and i need recommendations of books with a good treatment on the different techniques of integration. I'd like a book with good exercises for self study and a exposure to integration of different functions like integrals involving logarithmic and trigonometric functions or integrals involving logarithmic and power functions.

For one specifically on integration I guess you could try 'inside interesting integrals' by Nahin? My old maths teacher used to rave about that one a lot, although I didn't read the whole thing yet.

Santiago24
PhDeezNutz
You might have already realized this for yourself but in case you haven’t I’ll say it:

1) U-substitution is related to the chain rule of differentiation

2) UV-substitution (or integration by parts) is related to the product rule of differentiation

For UV-substitution there is a general rule of thumb for which function you want to make equal to ##u## in that order.

Log, Inverse Trig, Algebraic, Trig, Exponential.

1) and 2) might be regarded as trivial by some but if you don’t know them calculus becomes WAY more difficult.

Santiago24
Santiago24
For one specifically on integration I guess you could try 'inside interesting integrals' by Nahin? My old maths teacher used to rave about that one a lot, although I didn't read the whole thing yet.
I was looking on the internet and a lot of people recommend it and other book named "Irresistible Integrals" by George Boros, so i'll check it thanks.

etotheipi
Santiago24
You might have already realized this for yourself but in case you haven’t I’ll say it:

1) U-substitution is related to the chain rule of differentiation

2) UV-substitution (or integration by parts) is related to the product rule of differentiation

For UV-substitution there is a general rule of thumb for which function you want to make equal to ##u## in that order.

Log, Inverse Trig, Algebraic, Trig, Exponential.

1) and 2) might be regarded as trivial by some but if you don’t know them calculus becomes WAY more difficult.
Hi thanks for the information, my problem with the integration of trigonometric functions is that they use a lot of identities or formulas that i don't know where they come.

PhDeezNutz
Gold Member
What is your calculus background? You seem to be gravitating towards “how to solve hard integrals” but your statements seem more “how to address these weaknesses”

PhDeezNutz and Santiago24
Santiago24
What is your calculus background? You seem to be gravitating towards “how to solve hard integrals” but your statements seem more “how to address these weaknesses”
Hi I'm self studying calculus with the Spivak book. Yes, i have problems with integration by substitution because when i have to replace for u i don't know how to make appear du.

Gold Member
If u=f(x), du=f’(x)dx

You need to go through a calculus book for non-mathematicians. Given that you are getting theory from Spivak, there are probably sections you can glance through, but you should work every integration problem (most can be done in a couple of minutes). My openstax suggestion still stands or the first @micromass reference. If you live in a university town, you could get a cheap used copy of whatever they are using.

Santiago24
Gold Member
BTW, you do not need solutions for indefinite integrals. You can always take the derivative to check your work.

PhDeezNutz and Santiago24