integral of (csc^2(x)-a^x)

Lösung

\int (csc^{2} (x) - a^{x}) d x

- cot (x) - \frac{a ^{x}}{ln ( a )} + C

Schritte zur Lösung

\int csc^{2} (x) - a^{x} d x

Wende die Summenregel an:

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

= \int csc^{2} (x) d x - \int a^{x} d x

\int csc^{2} (x) d x = - cot (x)

\int a^{x} d x = \frac{a ^{x}}{ln ( a )}

= - cot (x) - \frac{a ^{x}}{ln ( a )}

Füge eine Konstante zur Lösung hinzu

= - cot (x) - \frac{a ^{x}}{ln ( a )} + C

x \to \infty lim (0^{- x})

y^{^{''}} - 2 y^{^{'}} + 1 y = 0, y (0) = 5, y^{^{'}} (0) = 4

d er i v a t i v e ln (x - 9)

\frac{\partial}{\partial x} ((x + 1)^{2} (x^{2} + 2 x))

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