Some integration questions (1 Viewer)

[ShadowHAwk]

Hello everybodi, im new here, and i got sum questions i got stuck wif while doing my homework... Show that 1+x/1-x = -1 + (2/1-x) and hence find the indefinite integral of 1+x/1-x with respect to x. Use the identity sec^2 theta = 1 + tan^2 theta to show that (indefinite integral sign) tan^2 theta with respect to theta = tan theta - theta + C any help with these questions is deeply appreciated =] thanks

 

[SoulSearcher]

1) -1 + (2/1-x) = [-(1-x) + 2]/(1-x)
= (-1+x+2)/(1-x)
= 1+x/1-x
You can integrate 1+x/1-x now

2) Let x = theta, its easier to write.
For number 2, just substitute sec²x - 1 = tan²x, then integrate with respect to theta, knowing that the integral of sec²x = tanx plus some constant.

 

[ShadowHAwk]

fanks for ur help!! but im still a bit confused in the 2nd question, after substituting sec^2x - 1, what do u do? im not sure wat u mean by integrating with respect to theta.. sorry

 

[SoulSearcher]

You would integrate as normal.

 

[Riviet]

∫tan²θ=∫(sec²θ-1)dθ since 1+tan²θ=sec²θ
=tanθ - θ + C