∫ x dx = ∫ x ( x + tan x) x + tan x dx = log | x + tan x| + c (or) = log |tan (π4 + x2)| + c ...

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First Principle of Differentiation

Solve ∫xdx=

Question

Solve $\int sec x d x =$

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Solution

$\int sec x d x = \int \frac{sec x (sec x + tan x)}{sec x + tan x} d x$

$= log | sec x + tan x | + c$
(or)
$= log | tan (\frac{π}{4} + \frac{x}{2}) | + c$

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