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1. Heres the question: Integrate (sec x)^2 (3tanx – 4)

I got this far

(1 + (tan x)^2)(3tanx - 4)

{using the trig identity (sec x)^2 = 1 + (tan x)^2}

Mulitplied it out:

3tanx - 4 + 3(tanx)^3 - 4(tanx)^2 dx

Is this correct so far, and to integrate would i just let x=tanx and go from there?

2. (Original post by HUPextreme)
Heres the question: Integrate (sec x)^2 (3tanx – 4)

I got this far

(1 + (tan x)^2)(3tanx - 4)

{using the trig identity (sec x)^2 = 1 + (tan x)^2}

Mulitplied it out:

3tanx - 4 + 3(tanx)^3 - 4(tanx)^2 dx

Is this correct so far, and to integrate would i just let x=tanx and go from there?

Integrate (sec x)^2 (3tanx – 4)
Let u = tanx here.
du/dx = sec^2x => du = sec^2x.dx

=> Integrate (sec x)^2 (3tanx – 4) dx
= Integrate (3u-4).du
= 3u^2/2 - 4u + c
= 1.5(tanx)^2 - 4tanx + c
3. oh cool, i didnt see that.

Thanks for the help, and for the swift reply.

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