integral of 2sqrt(t)-t-9/(t^2)

Lösung

\int 2 t - t - \frac{9}{t ^{2}} d t

\frac{4}{3} t^{\frac{3}{2}} - \frac{t ^{2}}{2} + \frac{9}{t} + C

Schritte zur Lösung

\int 2 t - t - \frac{9}{t ^{2}} d t

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int 2 t d t - \int t d t - \int \frac{9}{t ^{2}} d t

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

\int t d t = \frac{t ^{2}}{2}

\int \frac{9}{t ^{2}} d t = - \frac{9}{t}

= \frac{4}{3} t^{\frac{3}{2}} - \frac{t ^{2}}{2} - (- \frac{9}{t})

Vereinfache

= \frac{4}{3} t^{\frac{3}{2}} - \frac{t ^{2}}{2} + \frac{9}{t}

Füge eine Konstante zur Lösung hinzu

= \frac{4}{3} t^{\frac{3}{2}} - \frac{t ^{2}}{2} + \frac{9}{t} + C

x \to 0 lim (x^{2} - 4)

\int \frac{x ^{2}}{( 1 - y ^{2} )}

roo t s e^{a x}

\int (\frac{4}{x} - \frac{16}{x ^{2}}) d x

\frac{\partial}{\partial y} (\frac{e ^{y}}{x + y ^{9}})