integral of 2/3 x^{3/2}-9sin(x)

Lösung

\int \frac{2}{3} x^{\frac{3}{2}} - 9 sin (x) d x

\frac{4}{15} x^{\frac{5}{2}} + 9 cos (x) + C

Schritte zur Lösung

\int \frac{2}{3} x^{\frac{3}{2}} - 9 sin (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 \frac{2}{3} x^{\frac{3}{2}} d x - \int 9 sin (x) d x

\int \frac{2}{3} x^{\frac{3}{2}} d x = \frac{4}{15} x^{\frac{5}{2}}

\int 9 sin (x) d x = - 9 cos (x)

= \frac{4}{15} x^{\frac{5}{2}} - (- 9 cos (x))

Vereinfache

= \frac{4}{15} x^{\frac{5}{2}} + 9 cos (x)

Füge eine Konstante zur Lösung hinzu

= \frac{4}{15} x^{\frac{5}{2}} + 9 cos (x) + C

\frac{\partial}{\partial x} (7 x sin (y - z))

\int 3 x^{2} - 2 y^{2} d x

\int \frac{x}{1 - 2 x} d x

x \to 1 lim (3 + f (x))