What is the integral of 1/((1+x)^{0.5)} ?

The integral of 1/((1+x)^{0.5)} is x/(sqrt(1+x))+0.5(2sqrt(1+x)+2/(sqrt(1+x)))+C

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integral of 1/((1+x)^{0.5)}

integral

\frac{1}{( 1 + x ) ^{0.5}}

\frac{x}{1 + x} + 0.5 (2 1 + x + \frac{2}{1 + x}) + C

Solution steps

\int \frac{1}{( 1 + x ) ^{0.5}} d x

Apply Integration By Parts

: \frac{x}{( 1 + x ) ^{\frac{1}{2}}} - \int - \frac{0.5 x}{( 1 + x ) ^{1.5}} d x

= \frac{x}{( 1 + x ) ^{\frac{1}{2}}} - \int - \frac{0.5 x}{( 1 + x ) ^{1.5}} d x

\int - \frac{0.5 x}{( 1 + x ) ^{1.5}} d x = - 0.5 (2 1 + x + \frac{2}{1 + x})

= \frac{x}{( 1 + x ) ^{\frac{1}{2}}} - (- 0.5 (2 1 + x + \frac{2}{1 + x}))

Simplify

\frac{x}{( 1 + x ) ^{\frac{1}{2}}} - (- 0.5 (2 1 + x + \frac{2}{1 + x})) : \frac{x}{1 + x} + 0.5 (2 1 + x + \frac{2}{1 + x})

= \frac{x}{1 + x} + 0.5 (2 1 + x + \frac{2}{1 + x})

Add a constant to the solution

= \frac{x}{1 + x} + 0.5 (2 1 + x + \frac{2}{1 + x}) + C

2 sin (x) - x^{2} + 1

\frac{( x ^{2} + 4 )}{( x + 3 )}

f (x) = \frac{3 x + 3}{( 3 - 8 x + x ^{2} ) ^{\frac{1}{2}}}

x^{5} (x^{3} + 4)^{\frac{1}{2}}

x^{2} x \cdot 1

What is the integral of 1/((1+x)^{0.5)} ?
The integral of 1/((1+x)^{0.5)} is x/(sqrt(1+x))+0.5(2sqrt(1+x)+2/(sqrt(1+x)))+C