integration 1 + tan^2x

[woghd4390]

i still don't understand.

even though the answer is tanx...

integration of 1 + tan^2x can be written x + tan^3/3 isn't it?



anyone help plz

 

[Adif]

$\displaystyle \int (1+\tan^2 x)\ dx = \int \sec^2 x\ dx = \tan x + C.$

 

[stapel]

i still don't understand.

even though the answer is tanx...

integration of 1 + tan^2x can be written x + tan^3/3 isn't it?

Sure it can --- as long as "x + (1/3)tan^3(missing argument)" differentiates back to the original integrand. Does it?

 

[Steven G]

i still don't understand.

even though the answer is tanx...

integration of 1 + tan^2x can be written x + tan^3/3 isn't it?



anyone help plz

Integral of u^2 is NOT (u^3)/3 +c. Rather, integral of (u^2)du = (u^3)/3 + c.

In (tan^2)x your 1st mistake is not writing dx. Note that dx is NOT always du!!!!!
If you let u=tanx in integral (tan^2)x you get integral u^2 dx which is not (u^3)/3 + c since du= sec^2x dx