Question

Integretion Of cotX​

Answer 1

Answer:

To integrate cot(), recall that

cot()=cos()sin(),

so

∫cot()=∫cos()sin().

By choosing =sin(), that is, “=cos()” (in quotation marks because this expression does not make sense mathematically, but it does work formally), we get

∫cos()sin()=∫1=log()+=log(sin())+

Answer 2

★given:-

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

★Find:

• given quantity value

★SOLUTION:-

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

we know that

$\implies \pink{ \cot \theta = \frac{ \cos \theta}{ \sin \theta }}$

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

$\implies \: Let \: \sin x = t - - - (2)$

now EQ 2 differenciation

$\implies \: \frac{d}{dx} \sin \: x = dt\\ \\ \\ \implies \: \cos \: dx = dt - - (3)$

now equition (2 )and (3 )value put on EQ (1)

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

we know that

$\implies \pink{ \int \: \frac{1}{x}dx = log \: x }$

$\implies \: log(t)$

EQ 2 value put to we get

$\implies log | \sin \: x| + c$

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I hope it helps you