What is the integral from 0 to x of sqrt(2/(1+t)) ?

The integral from 0 to x of sqrt(2/(1+t)) is 2sqrt(2)sqrt(1+x)-2sqrt(2)

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integral from 0 to x of sqrt(2/(1+t))

\int_{0}^{x} \frac{2}{1 + t} d t

22 1 + x - 22

Solution steps

\int_{0}^{x} \frac{2}{1 + t} d t

Apply Integration By Parts

: [\frac{2}{1 + t} t - \int - \frac{t}{2 ( t + 1 ) ^{\frac{3}{2}}} d t]_{0}^{x}

= [\frac{2}{1 + t} t - \int - \frac{t}{2 ( t + 1 ) ^{\frac{3}{2}}} d t]_{0}^{x}

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

= [\frac{2}{1 + t} t - (- \frac{2 ( t + 2 )}{t + 1})]_{0}^{x}

Simplify

[\frac{2}{1 + t} t - (- \frac{2 ( t + 2 )}{t + 1})]_{0}^{x} : [22 1 + t]_{0}^{x}

= [22 1 + t]_{0}^{x}

Compute the boundaries:

22 1 + x - 22

= 22 1 + x - 22

\frac{d}{d x} (cos^{3} (5 x + 1))

y^{^{''}} + 4 y = - 6, y (\frac{π}{8}) = - 12, y^{^{'}} (\frac{π}{8}) = 2

\frac{d}{d x} ((x - 1) e^{- x})

\frac{d}{d x} (e^{3 x y})

h \to 0 lim (\frac{( f ( h ) ( 4 + h ) - f ( 4 ) )}{h})

What is the integral from 0 to x of sqrt(2/(1+t)) ?
The integral from 0 to x of sqrt(2/(1+t)) is 2sqrt(2)sqrt(1+x)-2sqrt(2)