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Home  >>  CBSE XII  >>  Math  >>  Integrals
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Find the integral $\int\sec x(\sec x+\tan x)dx$

$\begin{array}{1 1}\tan x+\sec x+c \\ \cot x+\sec x+c \\ \tan x+\cos x+c \\ \tan x+\sin x+c\end{array}$

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  • $(i)\;\int sec^2xdx=\tan x+c$.
  • $(ii)\;\int sec x\tan xdx=sec x+c$.
$\int sec x(sec x+\tan x)dx=\int \sec^2xdx+\sec x\tan x dx$.
$\qquad\qquad\qquad\qquad\;=\tan x+\sec x+c.$

Hence $\int sec x(sec x+\tan x)dx=\tan x+\sec x+c.$

answered Jan 27, 2013 by sreemathi.v
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