Question

what is the integration of ∫e²ⁿdn
please give answer.I am just get confused​

Answer 1

$\displaystyle \int {e}^{2n} dn$

Let , 2n = t

$\implies2n \: = t$

$\implies2 \: dn \: = dt$

$\implies\: dn \: = \dfrac{dt}{2}$

Now put dn = dt/2 :-

$\implies\displaystyle \int {e}^{2n} dn = \displaystyle \int {e}^{t} \frac{dt}{2}$

$\implies \displaystyle \int {e}^{t} \frac{dt}{2}$

$\implies \dfrac{1}{2} \displaystyle \int {e}^{t} {dt}$

$\implies \dfrac{1}{2} {e}^{t} + c$

where c is constant.

$\implies \dfrac{{e}^{t}}{2} + c$

Now put 2n = t :-

$\implies \dfrac{ {e}^{2n} }{2} + c$

Answer :

$\dfrac{ {e}^{2n} }{2} + c$

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

∫ 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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