Question

Q:-prove that:-
$∫secxdx = log |secx + tanx| + c$
solve step by step
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Answer 1

$\green{\bold{\underline{ ☆ UPSC-ASPIRANT ☆} }}$

$\red{\bold{\underline{\underline{QUESTION:-}}}}$

Q:-prove that:-

$∫secxdx = log |secx + tanx| + c$

$\huge\tt\underline\blue{ANSWER }$

------>>>>Here is your answer<<<<--------

⟹ $∫secxdx = log |secx + tanx| + c$

⟹ $∫secxdx =∫ \frac{secx(secx + </p><p>tanx)}{(secx + tanx)} dx$

⟹ $put \: secx + tanx = t$

⟹ $(secxtanx + {sec}^{2} x)dx = dt$

$secx(tanx + secx)dx = dt$

$⟹ ∫ \frac{dt}{t}$

$⟹ log |t| + c$

$⟹ log |secx + tanx| + c$✓

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