Question

integrate the given​

Answer 1

Answer:

$\large{ \bold{x - \frac{4}{x} + c}}$

Explanation:

$\int \frac{ {x}^{2} + 4}{ {x}^{2} } dx \\ \\ = \int \: (1 + \frac{4}{ {x}^{2} } )dx \\ \\ = \int1.dx + 4\int \: \frac{1}{ {x}^{2} } dx \\ \\ = x - \frac{4}{x} + c$

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Answer 2

$\implies\displaystyle \int \dfrac{ {x}^{2} + 4 }{ {x}^{2} }dx$

$\implies\displaystyle \int (\dfrac{ {x}^{2} }{ {x}^{2} } + \dfrac{ 4 }{ {x}^{2} })dx$

$\implies\displaystyle \int (1+ \dfrac{ 4 }{ {x}^{2} })dx$

$\implies\displaystyle \int 1dx+ \int\dfrac{ 4 }{ {x}^{2} }dx$

$\implies\displaystyle \int 1dx+ \int\dfrac{ 4{x}^{ - 2} }{ 1 }dx$

$\implies\displaystyle \int 1dx+ \int{ 4{x}^{ - 2} }dx$

$\implies\displaystyle x - { 4{x}^{ - 1} } + c$

where c is constant.

$\implies\displaystyle x - { \dfrac{4}{x} } + c$

Answer :

$\implies\displaystyle x - { \dfrac{4}{x} } + c$

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∫ ex dx = ex+ C

∫ ax dx = (ax/ln a) + C

∫ 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

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