Integral Calculus ( integrate by u-substitution) Note: S = integrate symbol S (x- 1/x)^2 dx?

I would like to know when to use u-substitution and of this is applicable

I would like to know some rules in using u-substitution this would really help me
Anyway this is needed for today thanks for your help!!!


1
less than 10 minutes daw may sagot na 3 hours na wla pa
aw sorry for my term anyway thanks

Answers

2014-05-17T01:15:45+08:00

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Usually, u sub is used when you find a suitable u such that it is easy to differentiate and its derivatives will be seen as factors of f. In this problem, using u sub would only make it more complicated.

If we expand it, we'll get

∫  \frac{ x^2-2x+1}{ x^2 } dx

= ∫  \frac{ x^2 }{  x^2 } dx - ∫  \frac{-2x}{  x^2  } dx + ∫ 1/x² dx

= ∫ dx + 2∫ 1/x dx + ∫1/x² dx

= x +2lnx -1/x
0
Please disregard the A's.
Also, i think u sub is used when the denominator has more than one terms