what is the integral of tan x?

Answer 1

∫tanx dx
= ∫sinx/cosx dx
= ∫-1/cosx dcosx
= -ln|cosx| + c
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Attention:
You need to have the absolute sign in your answer because if cosx is negative, lncosx is undefined.

Answer 2

Let tanx be the equation of the gradient function of a curve.
Now several asymptotes are seen here. That means the curve steeps up to gradients of + or - infinity very often for several values of x.
Integration of tanx means integration of the gradient function of the curve to find the equation of the curve without the specific y-intercept by taking it as an arbitrary unit "c".

Such curve I believe is like the tanx curve!

What do you reckon???
Or never thought this way!!??

Answer 3

integral of tan x
= -ln(cos x) + C or ln(sec x) + C

Answer 4

Write it as sinx / cosx

Now let u = cosx
du = -sinx dx

So you have to integrate -du/u
to get -ln(u) = ln(1/u)
= ln(secx)

Answer 5

∫ tanx dx = ∫ (sinx/cosx) dx

Let u = cosx ==> du = -sinx dx.

∫ tanx dx = ∫ (1/u)(-du)

∫ tanx dx = - ∫ du/u

∫ tanx dx = - log(u) + C

∫ tanx dx = log(1/u) + C

∫ tanx dx = log|1/cosx| + C

∫ tanx dx = log|secx| + C

Answer 6

I = ∫ (sin x / cos x) dx
I = - log (cos x) + C