integral of (1-cos(x))^{1/2}

Lösung

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

- 2 (cos (x) + 1)^{\frac{1}{2}} + C

Schritte zur Lösung

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

Wende U-Substitution an

= \int - \frac{1}{u + 1} d u

Entferne die Konstante:

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

= - \int \frac{1}{u + 1} d u

Wende U-Substitution an

= - \int \frac{1}{v} d v

Vereinfache

\frac{1}{v} : \frac{1}{v}

= - \int \frac{1}{v} d v

Vereinfache

= - \int \frac{1}{v} d v

Wende die Potenzregel an

= - 2 v^{\frac{1}{2}}

Ersetze zurück

= - 2 (cos (x) + 1)^{\frac{1}{2}}

Füge eine Konstante zur Lösung hinzu

= - 2 (cos (x) + 1)^{\frac{1}{2}} + C

\int \frac{sin ( 8 x )}{1 + cos ^{2} ( 8 x )} d x

l a pl a ce t r an s f or m 10

\frac{\partial}{\partial y} (x^{7} + 2^{y} + x^{y})

a re a x^{2} + 2 x, 2 x + 1

x \to 0 lim (\frac{x}{∣ x ∣})