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

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

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

integral

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

- \frac{x}{1 + x} + arctan (x) + C

Solution steps

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

Apply Integration By Parts

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

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

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

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

Simplify

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

Add a constant to the solution

= - \frac{x}{1 + x} + arctan (x) + C

y sin (y^{2})

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

\frac{1}{( t - 2 ) ^{2} + 16}

sec^{5} (x)

\frac{( x - y )}{( x + y ) ^{3}}

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