What is the integral of (sqrt(x+4))/(x^2) ?

The integral of (sqrt(x+4))/(x^2) is -(sqrt(x+4))/x-1/4 (ln|(sqrt(x+4))/2+1|-ln|(sqrt(x+4))/2-1|)+C

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integral of (sqrt(x+4))/(x^2)

\int \frac{x + 4}{x ^{2}} d x

- \frac{x + 4}{x} - \frac{1}{4} (ln \frac{x + 4}{2} + 1 - ln \frac{x + 4}{2} - 1) + C

Solution steps

\int \frac{x + 4}{x ^{2}} d x

Apply Integration By Parts

= - \frac{x + 4}{x} - \int - \frac{1}{2 x x + 4} d x

\int - \frac{1}{2 x x + 4} d x = \frac{1}{4} (ln \frac{x + 4}{2} + 1 - ln \frac{x + 4}{2} - 1)

= - \frac{x + 4}{x} - \frac{1}{4} (ln \frac{x + 4}{2} + 1 - ln \frac{x + 4}{2} - 1)

Add a constant to the solution

= - \frac{x + 4}{x} - \frac{1}{4} (ln \frac{x + 4}{2} + 1 - ln \frac{x + 4}{2} - 1) + C

What is the integral of (sqrt(x+4))/(x^2) ?
The integral of (sqrt(x+4))/(x^2) is -(sqrt(x+4))/x-1/4 (ln|(sqrt(x+4))/2+1|-ln|(sqrt(x+4))/2-1|)+C