Question

intigration of cotx​

Answer 1

★GIVEN:-

$\implies \int{ \cot \: x \: dx }$

★find:-

given quantity value

★solution:-

$\implies \int \: \cot \: x \: dx$

we know that

cot x= cos x /sin x

$\implies \int \: \frac{ \cos \: x }{ \sin\: x } dx - - - (1)$

let

sin x= t----------(2)

EQ 2 value put on EQ 1

$\implies \: \int \: \frac{ \cos \: x \: dx }{t} - - (3)$

sin x= t differciation with respect to x

$\implies \: \frac{d}{dx} \sin x = \frac{d}{dt} (t)$

we know that

$\implies \pink{ \frac{d}{dx} \sin \: x = \cos \: x }$

$\implies \: \cos \: x \: dx = dt - - - (4)$

equition (4) value put on EQ (3)

$\implies \int \: \frac{dt}{t}$

we know that

$\implies \pink{\int \: \frac{1}{x} = log |x| + c }$

$\implies \: log |t| + c - - - (5)$

equition (2) value put on EQ (5)

$\implies \pink{ log | \sin \: x | + c}$

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I hope it helps you