intergrate (1+tanx)^2?

Question

Give it a go! i know ul love it

Answer 1

It's not that difficult:

2*ln(sec(x)) + tan(x) + C

email me for the steps

Answer 2

Permit my use of S for the elognated S in the integral.
Then,
S (1+tan x)^2 dx = S (1+2tan x + tan^2 x) dx
= S (sec^2 x + 2tan x) dx
= tan x + 2.ln |sec x| + c

where c is an arbitrary constant of integration.

Answer 3

intergrate (1+tanx)^2
= (1+tanx)^3 / 3(secx)^2

Answer 4

If you expand it out you get

int 1 + 2 tan(x) + tan^2(x) dx
int (1+tan^2(x)) + 2 tan(x) dx
int sec^2(x) + 2 tan(x) dx
= tan(x) - 2 ln|cos(x)| + C

where C is any constant.

Answer 5

int{(1+tanx)^2}dx
=int{tan^x+2tanx+1}dx[expand]
= -x+tanx-2ln(cosx)+x+C
=tanx-2*ln(cosx)+C

whereC=a constant

{from standard tables
int(tan^2(x)= -x+tanx)
int(tanx= -ln(cosx)}

i hope that this helps