Let's do some integrals! The good thing about integral is
(a) It requires some tricks to get it done, an interesting intellectual challenge.
(b) It is easy to check if I have got the right answer, even without the model answer, just differentiate it.
Problem:
∫dx√x+√x+1
Solution:
The trick is rationalizing:
∫dx√x+√x+1=∫dx√x+√x+1√x+1−√x√x+1−√x=∫(√x+1−√x)dx=23(x+1)32−23x32+C
(a) It requires some tricks to get it done, an interesting intellectual challenge.
(b) It is easy to check if I have got the right answer, even without the model answer, just differentiate it.
Problem:
∫dx√x+√x+1
Solution:
The trick is rationalizing:
∫dx√x+√x+1=∫dx√x+√x+1√x+1−√x√x+1−√x=∫(√x+1−√x)dx=23(x+1)32−23x32+C
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