integral of rivative of sin(x)

Lösung

\int \frac{d}{d x} (sin (x)) d x

x \frac{d}{d x} (sin (x)) - x cos (x) + sin (x) + C

Schritte zur Lösung

\int \frac{d}{d x} (sin (x)) d x

Wende die partielle Integration an

= x \frac{d}{d x} (sin (x)) - \int - x sin (x) d x

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

= x \frac{d}{d x} (sin (x)) - (x cos (x) - sin (x))

Vereinfache

= x \frac{d}{d x} (sin (x)) - x cos (x) + sin (x)

Füge eine Konstante zur Lösung hinzu

= x \frac{d}{d x} (sin (x)) - x cos (x) + sin (x) + C

\int \frac{6 - 2 x}{16 + 6 x - x ^{2}} d x

\int 4 sin^{3} (2 x) cos^{2} (2 x) d x

\int cot^{4} (6 x) d x

\int \frac{1}{x ^{3} - 8 x ^{2} + 21 x - 18} d x

\int \frac{2 x ^{2} + 2 x - 9}{x ^{2} - 4} d x