Question

Integral tan^x secx

Answer 1

got this from online....

Answer 2

you mean tan^2 x
right ?

Answer 3

Take the integral:
integral sec(x) (tan(x)+sec(x))

Answer 4

xpanding the integrand sec(x) (tan(x)+sec(x)) gives sec^2(x)+tan(x) sec(x):
= integral (sec^2(x)+tan(x) sec(x))

Answer 5

Integrate the sum term by term:
= integral sec^2(x) dx+ integral tan(x) sec(x) dx
For the integrand tan(x) sec(x), substitute u = sec(x) and du = tan(x) sec(x)

Answer 6

= integral 1 du+ integral sec^2(x) dx
The integral of sec^2(x) is tan(x):
= integral 1 du+tan(x)
The integral of 1 is u:
= u+tan(x)+constant
Substitute back for u = sec(x):
Answer:
tan(x)+sec(x)+constant

Answer 7

Yes that's what I meant sorry. ∫tan^2x secx dx. Thank you!

Answer 8

I was thinking to re-write tan^2x as "sec^2x-1"
then expand, and then do the integral term by term.

Answer 9

^^
that should work

Answer 10

did you try it already ?