integral of (3t-2)/(sqrt(9-t^2))

Lösung

\int \frac{3 t - 2}{9 - t ^{2}} d t

- 3 9 - t^{2} - 2 arcsin (\frac{1}{3} t) + C

Schritte zur Lösung

\int \frac{3 t - 2}{9 - t ^{2}} d t

Multipliziere aus

\frac{3 t - 2}{9 - t ^{2}} : \frac{3 t}{9 - t ^{2}} - \frac{2}{9 - t ^{2}}

= \int \frac{3 t}{9 - t ^{2}} - \frac{2}{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 \frac{3 t}{9 - t ^{2}} d t - \int \frac{2}{9 - t ^{2}} d t

\int \frac{3 t}{9 - t ^{2}} d t = - 3 9 - t^{2}

\int \frac{2}{9 - t ^{2}} d t = 2 arcsin (\frac{1}{3} t)

= - 3 9 - t^{2} - 2 arcsin (\frac{1}{3} t)

Füge eine Konstante zur Lösung hinzu

= - 3 9 - t^{2} - 2 arcsin (\frac{1}{3} t) + C

\int arcsec (x) d x

x \to - 4 - lim (x^{2} + \frac{5}{x + 4})

\int \frac{1}{1 - 0.5 x} d x

x \to 10 - lim (8 - x)

\frac{\partial}{\partial z} (x e^{z} + x y + z^{3} - 4)