1-1-2x-dx-

Question Number 153563 by ZiYangLee last updated on 08/Sep/21

\int \frac{1}{1 + \sqrt{2 x}} d x = ?

Answered by puissant last updated on 08/Sep/21

u = \sqrt{2 x} \to u^{2} = 2 x \to x = \frac{u^{2}}{2} \Rightarrow d x = u d u

K = \int \frac{1}{1 + \sqrt{2 x}} d x = \int \frac{u}{1 + u} d u

= \int (1 - \frac{1}{1 + u}) d u

= u - l n ∣ 1 + u ∣ + C

∴∵ K = \sqrt{2 x} - l n ∣ 1 + \sqrt{2 x} ∣ + C . .

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