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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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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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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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 ...
• 1,471
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 ...
• 559
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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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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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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### (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 ...
1 vote
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 ...
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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1 vote