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

Lösung

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

- \frac{1 + x ^{2}}{x} + ln x^{2} + 1 + x + C

Schritte zur Lösung

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

Wende die partielle Integration an

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

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

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

Vereinfache

= - \frac{1 + x ^{2}}{x} + ln x^{2} + 1 + x

Füge eine Konstante zur Lösung hinzu

= - \frac{1 + x ^{2}}{x} + ln x^{2} + 1 + x + C

\int \frac{x ^{3} + x}{( x ^{2} + 3 ) ( x ^{2} - 2 x + 3 )} d x

\int e^{2 x} 1 + e^{x} d x

x \to 0 lim (\frac{x - sin ( x )}{x})

\frac{\partial}{\partial y} (y sin (y))

d er i v a t i v e y = 8 x sin (x^{2})