Question

Using the method of replacing show that ∫tan(x)=dx=In|sec(x)|+constantSee correction

Accepted Answer

To evaluate this integral, it is best to remember that tanx=sinx/cosx , which suggests the substitution u=cosx .  This means that du=-sinxdx , so the integral becomes:
int tanxdx 
=int sinx/cosx dx 
=-int 1/udu   now integrate using logarithm rule
=-ln|u|+C  where C is a constant of integration
=-ln|cosx|+C   now switch negative 1 to exponent
=ln|cosx|^{-1}+C   use trig definition of secx .
=ln|secx|+C 
The integral evaluates to ln|secx|+C .

Answer

Math

Using the method of replacing show that ∫tan(x)=dx=In|sec(x)|+constant See correction

Expert Answers

We’ll help your grades soar

Related Questions

Q. If `y =` `log{tan(pi/4 + x/2)}` , show that `dy/dx` - `sec x` = 0.

Prove that `sec^4(x)-tan^4(x)=1+tan^2(x)` .

Prove that (tan x)' = sec^2 x

sec^2 x - sec^2 y = tan^2 x - tan^2 y

Integral of sec^n(x)dx