Question

integration( x^4/4)dx​

Answer 1

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

$\implies \dfrac{ {x}^{(4 + 1)} }{4{(4 + 1)}} + c$

where c is constant.

$\implies \dfrac{ {x}^{(5)} }{4 \times {5}} + c$

$\implies \dfrac{ {x}^{5} }{20} + c$

Answer :-

$\implies \dfrac{ {x}^{5} }{20} + c$

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VERIFICATION OF ANSWER :-

If we differentiate ( x⁵/20+c) then we will get x⁴/4.

$\implies \dfrac{d( \dfrac{ {x}^{5} }{20})}{dx} + \dfrac{d(c)}{dx}$

$\implies 5 \times \dfrac{ {x}^{4} }{20} + 0$

$\implies \dfrac{ {x}^{4} }{4}$

hence verified

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$\large\bf\blue{Additional-Information}$

∫ 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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