Question

integral help

Answer 1

Sure!

Answer 2

\[\int\limits_{}^{} \tan^2 x \sec^2 x dx\]

Answer 3

You need some trig trick and then u sub.

Answer 4

i'm tryi

Answer 5

ing to figure out the trig trick

Answer 6

Remember that tan^2-1=sec^2

Answer 7

if u= tan x
du =... ?

Answer 8

du= sec x
?

Answer 9

no, what you get after differentiating, tan x .. ?
its pretty standard.

Answer 10

cos?

Answer 11

if u=tan x,
thn du= sec^2 x dx

Answer 12

ok, you need to revise all your differentiation formulas again....
d/dx (tan x) = sec^2 x

Answer 13

so, if u= tan x, du = sec^2x dx

Answer 14

\(\int\limits_{}^{} \tan^2 x (\sec^2 x dx) = \int u^2 du\)
can you solve that ?

Answer 15

yeah.
so tan x = u
and sec x =du
so it would be
\[ \frac{ u ^{3} }{ 3 } + c\]

Answer 16

then (tan ^3)/3 +c

Answer 17

right?

Answer 18

and resubstitute back u= tan x

Answer 19

yes, thats correct