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

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

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

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

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

Solution steps

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

Apply Integration By Parts

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

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

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

Simplify

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

Add a constant to the solution

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

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