Question

integral tan^5(x)dx

Answer 1

I wrote the method on the earlier posted question, if you need help using the formula let me know.

Answer 2

i cant use the formula

Answer 3

The 'trick' here is to step this down to the integral of tan^(something less than 5) x dx.

And the way to do that is to observe that
\[ (\tan x)' = \sec^2 x \] and \[ 1 + tan^2 x = sec^2 x. \]

So use those two results and try to rewrite your integral in such a way that you can integrate different parts.

The final answer for you is going to take a few steps, so be patient.

If I were you and I'd not seen this sort of problem before, I would try and find this integral first, as it will show you the method you need and the result in itself we be helpful: \[ \int \tan^3 x \ dx \]

Answer 4

what if i use the double angle identiy for tan, would that make it easier

Answer 5

No, I don't think so, because you'll end up with a fraction of trig functions.

Answer 6

correction: "the result in itself WILL be helpful"

Answer 7

i only get to the part where i break it up as integral tan^2(x)*tan^3(x)

Answer 8

calculate the integral of tan^3 x. Here's a big hint:
\[ \int \tan^3 x \ dx = \int \tan x (\sec^2 x - 1) \ dx \]
\[ = \int \tan x . \sec^2 x \ dx - \int \tan x \ dx \]

Answer 9

but i cant just calculuate the integral of tan^3x, since it is multiplied with tan^2(X)

Answer 10

oh i think i see

Answer 11

yup i def. see it now thanks man