integral of (sin^2(x)-4)/(sin(x)+2)

Lösung

\int \frac{sin ^{2} ( x ) - 4}{sin ( x ) + 2} d x

- cos (x) - 2 x + C

Schritte zur Lösung

\int \frac{sin ^{2} ( x ) - 4}{sin ( x ) + 2} d x

Vereinfache

\frac{sin ^{2} ( x ) - 4}{sin ( x ) + 2} : sin (x) - 2

= \int sin (x) - 2 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 sin (x) d x - \int 2 d x

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

\int 2 d x = 2 x

= - cos (x) - 2 x

Füge eine Konstante zur Lösung hinzu

= - cos (x) - 2 x + C

\int \frac{1}{x ^{3} - 7 x + 6} d x

\int \frac{4 x ^{2} - 4 x + 24}{x ^{3} + 3 x} d x

\int \frac{x e ^{x}}{9 + e ^{x}} d x

\int + \frac{4 y ^{2} - 7 y - 12}{y ( y + 2 ) ( y - 3 )} d y

\int 4 x^{2} e^{3 x^{2}} d x