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Beliebt Rechnen >

integral of (sin(x))/(5+cos^2(x))

Lösung

\int \frac{sin ( x )}{5 + cos ^{2} ( x )} d x

Lösung

- \frac{1}{5} arctan (\frac{cos ( x )}{5}) + C

Schritte zur Lösung

\int \frac{sin ( x )}{5 + cos ^{2} ( x )} d x

Wende U-Substitution an

= \int - \frac{1}{5 + u ^{2}} d u

Entferne die Konstante:

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

= - \int \frac{1}{5 + u ^{2}} d u

Wende integrale Substitution an

= - \int \frac{1}{5 ( 1 + v ^{2} )} d v

Entferne die Konstante:

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

= - \frac{1}{5} \cdot \int \frac{1}{1 + v ^{2}} d v

Nutze das gemeinsame Integral :

\int \frac{1}{1 + v ^{2}} d v = arctan (v)

= - \frac{1}{5} arctan (v)

Ersetze zurück

= - \frac{1}{5} arctan (\frac{cos ( x )}{5})

Füge eine Konstante zur Lösung hinzu

= - \frac{1}{5} arctan (\frac{cos ( x )}{5}) + C

Graph

Beliebte Beispiele

derivative of 1-|1-x|

\frac{d}{d x} (1 - ∣ 1 - x ∣)

integral of (x^4)/x

\int \frac{x ^{4}}{x} d x

limit as x approaches 2 of sin(1/(x-2))

x \to 2 lim (sin (\frac{1}{x - 2}))

limit as x approaches infinity of (4x^2+5x)/(sqrt(10+x^4))

x \to \infty lim (\frac{4 x ^{2} + 5 x}{10 + x ^{4}})

3 y^{^{''}} - 12 y = 0