Question

how we choose the function we let it equal u in integration by substitution ???
please any help

Answer 1

Choosing the right u-substitution can be extremely hard, since there isn't a lot of guidance for it. You have to know your derivatives pretty well. Basically the idea for a simple u-sub is to look at what's under the integral (called the integrand) and try to see if it can be split into a function and some multiple of it's derivative.

Answer 2

i.e.\[\int x\sqrt{x^2+5}dx\]notice that the part outside the radical, x, is *almost* like the derivative of what is under the radical
it's just off by a factor of 2, which can be fixed

Answer 3

this suggests we want u=(stuff under the radical), then go on to find out how to sub for xdx which remains outside

Answer 4

okay thank you very much ,i will practise more to do well

Answer 5

that's the key right there: practice :)