integral of (sqrt(x^2+25))/(x^2)

Lösung

\int \frac{x ^{2} + 25}{x ^{2}} d x

- \frac{x ^{2} + 25}{x} + ln (\frac{1}{5} x + 25 + x^{2}) + C

Schritte zur Lösung

\int \frac{x ^{2} + 25}{x ^{2}} d x

Wende die partielle Integration an

= - \frac{x ^{2} + 25}{x} - \int - \frac{1}{x ^{2} + 25} d x

\int - \frac{1}{x ^{2} + 25} d x = - ln (\frac{1}{5} x + 25 + x^{2})

= - \frac{x ^{2} + 25}{x} - (- ln (\frac{1}{5} x + 25 + x^{2}))

Vereinfache

= - \frac{x ^{2} + 25}{x} + ln (\frac{1}{5} x + 25 + x^{2})

Füge eine Konstante zur Lösung hinzu

= - \frac{x ^{2} + 25}{x} + ln (\frac{1}{5} x + 25 + x^{2}) + C

a re a x = y^{2}, x = 2 - y

t an g e n t f (x) = \frac{- 4 x}{x ^{2} + 1}, (- 1, 2)

d er i v a t i v e cos (θ^{2})

\int x (x^{2} + 4)^{5} d x

\frac{\partial}{\partial x} (e^{y x})