integral of (sin(2x))/(sqrt(1+cos^2(x)))

Lösung

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

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

Schritte zur Lösung

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

Wende U-Substitution an

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

Entferne die Konstante:

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

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

Wende die Potenzregel an

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

Setze in

u = 1 + cos^{2} (x)

ein

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

Wende Radikal Regel an:

a^{\frac{1}{n}} = n a

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

Füge eine Konstante zur Lösung hinzu

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

\frac{d y}{d x} = \frac{sec ( y )}{( x + 5 ) ^{2}}

\int \frac{1}{x ^{2} x ^{2} - 121} d x

\frac{d}{d x} (\frac{1 - c x}{1 + c x})

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

\frac{d y}{d x} = \frac{1}{3} x^{3}