Do you bother to integrate?

As time goes by in my physics career I find myself less and less motivated to do integrals by hand and more relying on integral tables to quickly look up the answer. I just find doing integration out by hand tedious, especially ones that require multiple integrations by parts or involve trig functions.

What are your thoughts on integrals?
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 Recognitions: Gold Member As long as you understand how you would go about solving the particular integrals, and you're not taking a class where you're graded on your ability to solve them by hand, why waste your time? Just look them up in a table or plug them in to a program. The only danger with doing this is when people with little experience with integrals don't know what the right answer should look like, so if the computer gives them a wrong answer they won't be able to recognize it. As long as you understand the process and have a general idea of how the answer should look, I don't see the harm in using programs/tables.
 Recognitions: Gold Member I have better things to do than waste time on integrals I've already done before.

Do you bother to integrate?

 Quote by dipole As time goes by in my physics career I find myself less and less motivated to do integrals by hand and more relying on integral tables to quickly look up the answer. I just find doing integration out by hand tedious, especially ones that require multiple integrations by parts or involve trig functions. What are your thoughts on integrals?
It is still best to do it if that is the first time you see such integrals.
 Recognitions: Science Advisor Tables? I just shove them in Mathematica.

 Quote by K^2 Tables? I just shove them in Mathematica.
Is there a free version of Mathematica?

Not a 30-day trial either.

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 Quote by Neandethal00 Is there a free version of Mathematica? Not a 30-day trial either.
Wolfram Alpha can do integrals I'm pretty sure. It's just not as easy to type out complex ones. You can probably get mathematica pretty cheap if you attend a university.
 Sometimes I've needed a general expression rather than a number, so I've had to solve integrals for that.
 Wolfram Alpha and a few others can do indefinite as well as definite integrals with arbitrary constants. The only trouble is typing the equation out correctly with complex equations... As for bothering to integrate, I don't if I already know how to integrate the expression, however long it might turn out. Its always fun to try out new, never-seen-before integrals!
 Try a calculator that does integrals like HP50g or TI89ti. The 50g has an Equation Writer so you see the expression written out in Pretty Type.

 Quote by Neandethal00 Is there a free version of Mathematica? Not a 30-day trial either.
MMA isn't free but Maxima is.

 Quote by Neandethal00 Is there a free version of Mathematica? Not a 30-day trial either.
Try Maxima, it is a FOSS project and works very well

http://maxima.sourceforge.net/

 Quote by viraltux Try Maxima, it is a FOSS project and works very well http://maxima.sourceforge.net/
Once you get Maxima you can use an editor like TeXmacs.

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 Quote by Neandethal00 Is there a free version of Mathematica?
A lot of universities have free licenses for their students. That's how I got my license. Otherwise, you have to pay or use an alternative program.

You can, indeed, do a lot of things with Wolfram Alpha, but if your integral times out, you are out of luck. For integrals, you can use Mathematica syntax to make sure Alpha doesn't screw up.
 Recognitions: Gold Member Science Advisor Trouble is that there is a risk of relying on the computer too much, to do your thinking for you. It must be good for people to go through the agony of basic integration and learning how to solve differential equations and not to reach for Mathematica before you even have an idea what it is doing for you. There's a similar problem with this new generation of students and the reliance on circuit simulation programs rather than using analysis methods even for the simplest problems. (And using calculators to multiply by 100!) I wouldn't be without computers to help me but I couldn't bring myself to rely entirely on what they tell me. After all, GIGA applies whenever computers are involved. You need to be able to recognise garbage when it comes out.

 Quote by sophiecentaur Trouble is that there is a risk of relying on the computer too much, to do your thinking for you. It must be good for people to go through the agony of basic integration and learning how to solve differential equations and not to reach for Mathematica before you even have an idea what it is doing for you. There's a similar problem with this new generation of students and the reliance on circuit simulation programs rather than using analysis methods even for the simplest problems. (And using calculators to multiply by 100!) I wouldn't be without computers to help me but I couldn't bring myself to rely entirely on what they tell me. After all, GIGA applies whenever computers are involved. You need to be able to recognise garbage when it comes out.
Yes I agree with this, which is why I prefer not to use Wolfram. At least with a table I may need to manipulate the integral slightly to get it into a desired form, which hopefully will make me more careful. With computers you can be exceptionally lazy.

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