integral of xcot^2(x)

Lösung

\int x cot^{2} (x) d x

- x^{2} - x cot (x) + \frac{x ^{2}}{2} + ln ∣ sin (x) ∣ + C

Schritte zur Lösung

\int x cot^{2} (x) d x

Wende die partielle Integration an

= x (- x - cot (x)) - \int - x - cot (x) d x

\int - x - cot (x) d x = - \frac{x ^{2}}{2} - ln ∣ sin (x) ∣

= x (- x - cot (x)) - (- \frac{x ^{2}}{2} - ln ∣ sin (x) ∣)

Vereinfache

x (- x - cot (x)) - (- \frac{x ^{2}}{2} - ln ∣ sin (x) ∣) : - x^{2} - x cot (x) + \frac{x ^{2}}{2} + ln ∣ sin (x) ∣

= - x^{2} - x cot (x) + \frac{x ^{2}}{2} + ln ∣ sin (x) ∣

Füge eine Konstante zur Lösung hinzu

= - x^{2} - x cot (x) + \frac{x ^{2}}{2} + ln ∣ sin (x) ∣ + C

\int \frac{1}{( 1 + 3 x ) x} d x

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

\int e^{x} (2^{x} - 1) d x

\int \frac{e ^{- x} - 1}{( e ^{- x} + x ) ^{2}} d x

\int sin (x) (sec^{2} (x) + cot^{2} (x)) d x