Substitution in Indefinite Integrals (sample questions and discussion)

hallo friends, meet again with me mr.Chem-Eng.21, in this moment i want to share about lesson calculus-1 about sustitution in indefinite integrals. in this chance i want to share exercise or example problem of this matter. Ok friends see and understand of this material:

SUBSTITUTION IN INDEFINITE INTEGRALS- If you face up to a indefinite integrals, and if formal form, immediately we get the result. if NO find a substitution that will change become a new form. if on first substitution, we not get the result formal form, we try with another way. if we have long practice , we will get find replacement which true.

EXAMPLES:

1. ∫xcos2(x2)dx.

Completion => formal form ∫sec2udu.if u = x2, du = 2x.dx

Then ∫xcos2(x2)dx = 12∫1cos2(x2).2xdx = 12∫sec2udu

 = 12tanu + C = 12tan(x2) + C

2. ∫3√5 − 9x2dx.

Completion => remember of form ∫du√a2 − u2if u = 3x

Then ∫3√5 − 9x2dx = ∫1√5 − u2du = sin − 1(u√5) + C

 = sin − 1(3x√5) + C

3. ∫6e1xx2dx

Completion, remember ∫eudu. if u = 1x, so du = ( − 1x2)dx

Then ∫6e1xx2dx =  − 6∫e1x( − 1x2dx) =  − 6∫eudu

 =  − 6eu + C =  − 6e1x + C

OK friends, so easy ok....haha i think for this time enough, only 3 examples for this moment and for continue example in others time/moment. hopefully this simple matter and simple solution of this problem/example can be help your problem in calculus or useful for all, and thanks for all your attention, and close wassalamualaikum wr,..good bye....