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

Popular >

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

= - \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

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

\int \frac{2 x ^{2} + 3}{x ^{4} - 2 x ^{2} + 1} d x

\int \frac{t ^{3}}{e ^{2 t^{4}}} d t

\int 4 x sinh (2 x) d x

\int \frac{1}{sin ( x ) + cos ( x ) + 3} d x

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