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

Lösung

\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

Schritte zur Lösung

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

Wende die partielle Integration an

= - \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)

Füge eine Konstante zur Lösung hinzu

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

\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

\int \frac{t + 1}{t ^{2} + 2 t + 3} d t