What is the Easiest Way to Solve an Integration Problem Involving Tan(x)?

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The easiest way to solve the indefinite integral involving tan(x) is to recognize that the derivative of tan(x) is sec²(x) and to use u-substitution. A user initially struggled with the problem but quickly realized the solution involves substituting u = tan(x). Another participant suggested a simpler substitution of u = tan(x) + 2, noting that the constant does not affect the derivative. This approach simplifies the integration process. The discussion highlights the importance of recognizing derivatives and effective substitution in solving integration problems.
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Solved. Thanks.
 
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The simplest way to solve that indefinite integral is to realize that

\frac{d}{dx}tan x = sec^{2}x , and try a u-substitution from there...
 
meiso said:
The simplest way to solve that indefinite integral is to realize that

\frac{d}{dx}tan x = sec^{2}x , and try a u-substitution from there...

Yes, sorry, i am stupid. I realized that 2 minutes after posting here. I'm pretty sure i have it now. It's just -(2+u)^{-1} for u=tanx, right? And thanks for the reply.
 
Noo said:
It's just -(2+u)^{-1} for u=tanx, right? And thanks for the reply.

No problem. And, actually, you can set u = tan(x) + 2 to make things even easier. 2 is just a constant, so the derivative of tan(x) is the same as the derivative of tan(x) + 2.
 

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