Integral of tan^4x

This calculus video tutorial explains how to find the integral of tan^4x using integration by u-substitution and pythagorean identities of secant and tangent.

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[rivalrimongaming]

You Tube had never been this helpful, all thanks to you sir.

[ok-ioxb]

you legit save my life thank you so so much

[jr.jackrabbit]

thank you so much, my textbook totally glossed over the distribution and separation, going from integral(tan^2x * (sec^2x -1)dx) directly into integral(sec^2xtan^2xdx) - integral(tan^2xdx)
i was so confused and figured there wouldn't be any resources to help me understand, and i'm glad i was wrong about that.

[ajaymeena]

Can you do a interigation on underroot tanx plz

[calisthenicsguy]

I got a question, why instead of replacing both tan^2x to sec^2x -1, you use the solution [sec^2x-1] tan^2 x dx?
if i use the first solution
[tan^2 x] [tan^2 x] dx, substitute the identity [sec^2 x - 1] [sec^2x -1] dx, FOIL method = integral of [sec^4 x dx - 2sec^2 x dx +1 ]dx
that would be equals to tan^2x -2tan x + x + c.

While if you use the method that you're doing the answer would be 1/3 tan^3 x - tan x + x +c ?

So my only question is, why didn't we substitute both tan^2x ?

[boomergen]

i just missed to not split the integrals and waited for a blank 30 mins to come up with new

[ichigor.]

the C's on the final answer dont cancel?