\[{logsec}x(\sec x + \tan x) + c] | MATH - FUNDAMENTAL INTEGRATION | SolveeIt

${logsec}x(\sec x + \tan x) + c$

$\int_{}^{}{\frac{2x}{(2x + 1)^{2}}dx =}$

$\frac{1}{2}\log(2x + 1) + \frac{1}{2(2x + 1)} + c$

$\frac{1}{2}\log(2x + 1) - \frac{1}{2(2x + 1)} + c$

$2\log(2x + 1) + \frac{1}{2(2x + 1)} + c$

Answer

$2\log(2x + 1) + \frac{1}{2(2x + 1)} + c$

Explanation

$\log(\cos^{- 1}x) + c$

$- \log(\cos^{- 1}x) + c$

$- \frac{1}{2(\cos^{- 1}x)^{2}} + c$

Question: \[{logsec}x(\sec x + \tan x) + c\]...