Question

integrate (3x^3-2√x)/x dx​

Answer 1

$\implies\displaystyle \int \dfrac{3 {x}^{3} - 2 \sqrt{x} }{x}dx$

$\implies\displaystyle \int \dfrac{3 {x}^{3} }{x}dx - \displaystyle \int\frac{2 \sqrt{x}}{x} dx$

$\implies\displaystyle \int \dfrac{3 {x}^{2} }{1}dx - \displaystyle \int\frac{2 {x}^{ \frac{1}{2} } }{x} dx$

$\implies\displaystyle \int \dfrac{3 {x}^{2} }{1}dx - \displaystyle \int\frac{2 {x}^{ \frac{1}{2} - 1} }{1} dx$

$\implies\displaystyle \int \dfrac{3 {x}^{2} }{1}dx - \displaystyle \int\frac{2 {x}^{ \frac{ - 1}{2} } }{1} dx$

$\implies\displaystyle \dfrac{3 {x}^{3} }{3} - \displaystyle \frac{{4 {x}^{ \frac{ 1}{2} } }{} }{1} + c$

$\implies\displaystyle \dfrac{ {x}^{3} }{1} - \displaystyle \frac{{4 {x}^{ \frac{ 1}{2} } }{} }{1} + c$

$\implies\displaystyle {x}^{3} - \displaystyle {{4 {x}^{ \frac{ 1}{2} } }{} } + c$

Answer :

$\implies\displaystyle {x}^{3} - \displaystyle {{4 {x}^{ \frac{ 1}{2} } }{} } + c$

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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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