Question

can someone please solve this question [integrate(3/x)dx]​

Answer 1

⟹$\int_{}^{} \dfrac{3}{x} dx$

⟹$3\int_{}^{} \dfrac{1}{x} dx$

We know that :-

⟹$\int_{}^{} \dfrac{1}{x} dx = log(x)$

therefore :-

⟹$3log(x) + c$

where c = constant

Answer :

$3log(x) + c$

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Learn more:

∫ 1 dx = x + C

∫ sin x dx = – cos x + C

∫ cos x dx = sin x + C

∫ sec2 dx = tan x + C

∫ csc2 dx = -cot x + C

∫ sec x (tan x) dx = sec x + C

∫ csc x ( cot x) dx = – csc x + C

∫ (1/x) dx = ln |x| + C

∫ ex dx = ex+ C

∫ ax dx = (ax/ln a) + C

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Answer 2

Given ,

The function is 3/x

integrating wrt to x , we get

$\tt \implies \int{ \frac{3}{x}} \: \: dx$

$\tt \implies 3 \int{ \frac{1}{x}} \: \: dx$

$\tt \implies 3 \times log(x) + C$

Remmember :

$\tt \implies \int{ {(x)}^{n} } \: \: dx = \frac{ {(x)}^{n + 1} }{n + 1}+ C \: \: , \: \: n≠1$

$\tt \implies \int{ \frac{1}{x} } \: \: dx = log(x) + C$

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