integral of (x^2)/(csc(x))

Lösung

\int \frac{x ^{2}}{csc ( x )} d x

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

Schritte zur Lösung

\int \frac{x ^{2}}{csc ( x )} d x

Verwende die grundlegende trigonometrische Identität:

\frac{1}{csc ( x )} = sin (x)

= \int x^{2} sin (x) d x

Wende die partielle Integration an

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

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

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

Vereinfache

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

Füge eine Konstante zur Lösung hinzu

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

\int_{0}^{5} \frac{1}{x ^{\frac{19}{20}}} d x

\int_{0}^{4} (6 - x^{2}) d x

d er i v a t i v e x^{2} - \frac{1}{2} cos (x)

d er i v a t i v e f (x) = (x^{4} + 3) (- 4 x^{5} + 5 x^{4} + 5)

d er i v a t i v e u