Question

Integral of tan^4 (x) * sec^2 (x) dx

Answer 1

derivative of tan(x) is ?

Answer 2

sec^2 (x)

Answer 3

yes, so your u-substitution is u= ?

Answer 4

- thats the way to go

Answer 5

Ohh, how do we determine the u substitution?

Answer 6

you know that for any
\[\int\limits_{ }^{ } F\left(~g(x)~\right)~~\times ~g'(x)~~dx\]
then you set:
u=g(x)
du=g'(x) dx
and you get:
\[\int\limits_{ }^{ } F\left(~u~\right) ~du\]

Answer 7

is this last post making sense?

Answer 8

YEsssss

Answer 9

thank you

Answer 10

tan^4(x) is same as (tan x)^4

Answer 11

so your u= ?

Answer 12

tanx

Answer 13

yes, and your new integral is ?

Answer 14

integral of tan^4(x) dx

Answer 15

Yes I understand now, thank you

Answer 16

no, not really...

Answer 17

\[\int\limits_{ }^{ } (\color{red}{\tan x})^4\cdot \color{green}{(\sec^2x)~dx}\]\[\int\limits_{ }^{ } (\color{red}{u})^4 \color{green}{du}\]

Answer 18

the red is our u-substitution and green is what "du" is