integral of (sqrt(9+x^2))/(x^4)

Lösung

\int \frac{9 + x ^{2}}{x ^{4}} d x

- \frac{9 + x ^{2}}{3 x ^{3}} - \frac{9 + x ^{2}}{27 x} + C

Schritte zur Lösung

\int \frac{9 + x ^{2}}{x ^{4}} d x

Wende die partielle Integration an

= - \frac{9 + x ^{2}}{3 x ^{3}} - \int - \frac{1}{3 x ^{2} x ^{2} + 9} d x

\int - \frac{1}{3 x ^{2} x ^{2} + 9} d x = \frac{9 + x ^{2}}{27 x}

= - \frac{9 + x ^{2}}{3 x ^{3}} - \frac{9 + x ^{2}}{27 x}

Füge eine Konstante zur Lösung hinzu

= - \frac{9 + x ^{2}}{3 x ^{3}} - \frac{9 + x ^{2}}{27 x} + C

\int_{0}^{1} (x^{2} + 1) e^{2 x} d x

t an g e n t 6 x^{2} - 4 x y + 4 y^{2} - 14 = 0, (1, 2)

t an g e n t y = x + 1, (8, 3)

d er i v a t i v e f (x) = x^{4} - 2 x^{3} + x - 1

\frac{d}{d t} (e^{r (t) t})