Question

integral of 2(tan x)(sec x)^2 dx = (tan x) ^2 = (sec x)^2? is this so?

Answer 1

Secant x and Tangent x are not the same thing, so no.

Answer 2

int 2 (tanx) (secx)^2 dx
= 2 int (tanx secx) secx dx
use int u-sub

let u = secx
du = secx tanx dx

see ur integral becomes
2 int u du
= ...

does that helps ?

Answer 3

\[\int\limits_{}^{}2 \tan x \sec ^{2}x dx \] if I put u = tan x, du = \(\sec ^{2} x dx\), so it will be \(\int\limits_{}^{}2u du= \frac{ 2u ^{2} }{ 2 }=u ^{2} = \tan ^{2}x\)
but if I use u=sec x, du = sec x tan x dx, so I get \(\int\limits_{}^{}2udu = \frac{ 2u ^{2} }{ 2 } = \sec^{2}x\)

Did I do something wrong?

Answer 4

no, u are right

the result is same, just different for the constant

Answer 5

oh I see, that's pretty interesting.

Answer 6

yeah, if we derive it
then will back to the original function :)