What are the mistakes here?

[Win_odd Dhamnekar]

How to do sanity checks in the following two examples?

 

[blamocur]

How to do sanity checks in the following two examples?

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1. [imath]\frac{1}{x^2}[/imath] is not integrable over segments containing 0, so you get what you get.
2. Indefinite integrals are defined up to a constant additive. If you differentiate both sides you'll get the same [imath]\frac{1}{x}[/imath]

 

[Dr.Peterson]

How to do sanity checks in the following two examples?

View attachment 32966

1. Graph the integrand, and ponder what you see.

2. What do you always have to add when you write the final answer?