The value of ∫ \sqrtx e^{\sqrtx} dx is equal to

Correct Answer is : (2x - 4 x + 4) ex + X

2\sqrtx - e^{\sqrtx} - 4 \sqrt{xe^{\sqrtx} + X

(2x - 4 \sqrtx + 4) e^{\sqrtx} + X

(2x + 4 \sqrtx + 4) e^{\sqrtx} + X

NIMCET 2014 Question Paper with solutions

Question : 6 of 120

Marks: +1, -0

The value of ∫

√x e^{√x}

dx is equal to

Solution:

We have , l =

∫ √x e^{√x}

dx ... (i)
put

√x

= t
⇒

1/{2√x}

dx = dx
⇒ dx = 2

√x

dt
∴ l = 2 ∫

√x e^t

t dt = 2 ∫

t^2 e^t

dt
= 2 [

t^2 . e^t - 2

∫

te^t

dt]
= 2

[t^2e^t-2(te^t-e^t)]

+ C
=

2e^t[t^2-2t+2]

+ C
=

e^{√x}

[2x - 4

√x + 4] + C

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