integral of 2cot^2(x)-3tan^2(x)

Lösung

\int 2 cot^{2} (x) - 3 tan^{2} (x) d x

x - 2 cot (x) - 3 tan (x) + C

Schritte zur Lösung

\int 2 cot^{2} (x) - 3 tan^{2} (x) 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 2 cot^{2} (x) d x - \int 3 tan^{2} (x) d x

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

\int 3 tan^{2} (x) d x = 3 (- x + tan (x))

= 2 (- x - cot (x)) - 3 (- x + tan (x))

Vereinfache

2 (- x - cot (x)) - 3 (- x + tan (x)) : x - 2 cot (x) - 3 tan (x)

= x - 2 cot (x) - 3 tan (x)

Füge eine Konstante zur Lösung hinzu

= x - 2 cot (x) - 3 tan (x) + C

\int (y - x)^{2} d x

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