integral of tan^2(x)x

Lösung

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

- x^{2} + x tan (x) + \frac{x ^{2}}{2} + ln ∣ cos (x) ∣ + C

Schritte zur Lösung

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

Wende die partielle Integration an

= x (- x + tan (x)) - \int - x + tan (x) d x

\int - x + tan (x) d x = - \frac{x ^{2}}{2} - ln ∣ cos (x) ∣

= x (- x + tan (x)) - (- \frac{x ^{2}}{2} - ln ∣ cos (x) ∣)

Vereinfache

x (- x + tan (x)) - (- \frac{x ^{2}}{2} - ln ∣ cos (x) ∣) : - x^{2} + x tan (x) + \frac{x ^{2}}{2} + ln ∣ cos (x) ∣

= - x^{2} + x tan (x) + \frac{x ^{2}}{2} + ln ∣ cos (x) ∣

Füge eine Konstante zur Lösung hinzu

= - x^{2} + x tan (x) + \frac{x ^{2}}{2} + ln ∣ cos (x) ∣ + C

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