What is the integral of sqrt(2/(x+1)) ?

The integral of sqrt(2/(x+1)) is sqrt(2/(x+1))x+(sqrt(2)(x+2))/(sqrt(x+1))+C

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integral of sqrt(2/(x+1))

\int \frac{2}{x + 1} d x

\frac{2}{x + 1} x + \frac{2 ( x + 2 )}{x + 1} + C

Solution steps

\int \frac{2}{x + 1} d x

Apply Integration By Parts

: \frac{2}{x + 1} x - \int - \frac{x}{2 ( x + 1 ) ^{\frac{3}{2}}} d x

= \frac{2}{x + 1} x - \int - \frac{x}{2 ( x + 1 ) ^{\frac{3}{2}}} d x

\int - \frac{x}{2 ( x + 1 ) ^{\frac{3}{2}}} d x = - \frac{2 ( x + 2 )}{x + 1}

= \frac{2}{x + 1} x - (- \frac{2 ( x + 2 )}{x + 1})

Simplify

= \frac{2}{x + 1} x + \frac{2 ( x + 2 )}{x + 1}

Add a constant to the solution

= \frac{2}{x + 1} x + \frac{2 ( x + 2 )}{x + 1} + C

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What is the integral of sqrt(2/(x+1)) ?
The integral of sqrt(2/(x+1)) is sqrt(2/(x+1))x+(sqrt(2)(x+2))/(sqrt(x+1))+C