integral of sin(x)sqrt(cos(x))

Lösung

\int sin (x) cos (x) d x

- \frac{2}{3} cos^{\frac{3}{2}} (x) + C

Schritte zur Lösung

\int sin (x) cos (x) d x

Wende U-Substitution an

= \int - u d u

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= - \int u d u

Wende die Potenzregel an

= - \frac{2}{3} u^{\frac{3}{2}}

Setze in

u = cos (x)

ein

= - \frac{2}{3} cos^{\frac{3}{2}} (x)

Füge eine Konstante zur Lösung hinzu

= - \frac{2}{3} cos^{\frac{3}{2}} (x) + C

\frac{\partial}{\partial y} (e^{x} \cdot cos (y))

t a y l or ln (2 x), 1

\frac{\partial}{\partial x} (e^{x} cos (θ))

t an g e n t f (x) = x^{4} - 6 x^{2} - x, at x = 1, y = 6

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