Linked Questions

9 votes
2 answers
543 views

Integration training? [duplicate]

I've been pretty frustrated lately with my poor integration skills. A lot of times I find that in my math or physics classes I understand the concepts behind a question, reduce it to an integral, and ...
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  • 367
0 votes
0 answers
109 views

The art of integration [duplicate]

I am a trivial high school student who loves maths. Recently I found some maths-related YouTube channels. Although they cover a broad range of mathematics, many of them are about integration. So I ...
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508 votes
10 answers
256k views

Integral $\int_{-1}^1\frac1x\sqrt{\frac{1+x}{1-x}}\ln\left(\frac{2\,x^2+2\,x+1}{2\,x^2-2\,x+1}\right) \mathrm dx$

I need help with this integral: $$I=\int_{-1}^1\frac1x\sqrt{\frac{1+x}{1-x}}\ln\left(\frac{2\,x^2+2\,x+1}{2\,x^2-2\,x+1}\right)\ \mathrm dx.$$ The integrand graph looks like this: $\hspace{1in}$ The ...
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129 votes
6 answers
46k views

Why is integration so much harder than differentiation?

If a function is a combination of other functions whose derivatives are known via composition, addition, etc., the derivative can be calculated using the chain rule and the like. But even the product ...
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  • 1,471
12 votes
7 answers
782 views

Where to find interesting integrals for a Calc III student?

I apologize in advance if this is a very soft question. I won't be surprised or offended if I can't get a good answer. One of my favorite things to do in my spare time, when I'm feeling analytical of ...
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  • 559
18 votes
1 answer
2k views

What would qualify as a valid reason to believe there is a closed form?

I noticed that almost every non-homework-level integral posted on this site prompts somebody to ask "Do you have any reason to believe there is a closed form?" (some recent examples here and here) I ...
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6 votes
3 answers
1k views

Where to learn integration techniques?

Is there any book or any website that let you learn integration techniques? I'm not talking about the standard ones like integration by Parts Substitution (trigonometric) Partial fractions Order ...
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8 votes
1 answer
729 views

References on integration: collections of fully worked problems (and explanations) of (1) advanced and (2) unusual techniques

I am searching for two kinds of books. (1) Comprehensive books that collect, explain, and provide many examples (that is, fully worked problems) of advanced integration techniques (that is, ...
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  • 7,666
2 votes
1 answer
1k views

(High school) How to become an expert on integration?

It is very hard for me sometimes to find a right method to do an integration, for example, whether to use by parts method or substitution. I always find the questions I was given on an exam very hard ...
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1 vote
0 answers
395 views

Favorite definite integral trick? [duplicate]

I'm compiling a list of interesting definite integrals for an upcoming blog post, and I thought that the math SE community might have a few interesting problems to offer. I am especially interested in ...
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2 votes
2 answers
299 views

Is it always true that no closed forms exists for any divergent series?

Having seen many questions regarding finding closed form of integrals or infinite series, and some users providing either the final answer or detailed solution, and also reading how one finds a closed ...
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  • 2,270
1 vote
1 answer
108 views

Integral evaluating techniques - Textbook

I was wondering if anyone can suggest a textbook that encapsulates a fairly large range of evaluating integrals. I find this particular subject quite intriguing and what to expand my knowledge of it . ...
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  • 3,106