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Beliebt Rechnen >

integral of 3xsec^2(3x)

Lösung

\int 3 x sec^{2} (3 x) d x

Lösung

3 (\frac{1}{2} x^{2} sec^{2} (3 x) - \frac{1}{18} (9 x^{2} tan^{2} (3 x) - 6 x tan (3 x) - 2 ln ∣ cos (3 x) ∣ + 9 x^{2})) + C

Schritte zur Lösung

\int 3 x sec^{2} (3 x) d x

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 3 \cdot \int x sec^{2} (3 x) d x

Umschreiben mit Hilfe von Trigonometrie-Identitäten

= 3 \cdot \int x (1 + tan^{2} (3 x)) d x

Wende die partielle Integration an

= 3 (\frac{1}{2} x^{2} sec^{2} (3 x) - \int 3 x^{2} sec^{2} (3 x) tan (3 x) d x)

\int 3 x^{2} sec^{2} (3 x) tan (3 x) d x = \frac{1}{18} (9 x^{2} tan^{2} (3 x) - 6 x tan (3 x) - 2 ln ∣ cos (3 x) ∣ + 9 x^{2})

= 3 (\frac{1}{2} x^{2} sec^{2} (3 x) - \frac{1}{18} (9 x^{2} tan^{2} (3 x) - 6 x tan (3 x) - 2 ln ∣ cos (3 x) ∣ + 9 x^{2}))

Füge eine Konstante zur Lösung hinzu

= 3 (\frac{1}{2} x^{2} sec^{2} (3 x) - \frac{1}{18} (9 x^{2} tan^{2} (3 x) - 6 x tan (3 x) - 2 ln ∣ cos (3 x) ∣ + 9 x^{2})) + C

Graph

Beliebte Beispiele

integral of 2/(x(x^2+6)^2)

\int \frac{2}{x ( x ^{2} + 6 ) ^{2}} d x

integral of 3/2 x2^x

\int \frac{3}{2} x 2^{x} d x

integral of (e^{5-(3y)/7})

\int (e^{5 - \frac{3 y}{7}}) d y

integral of (x-2)/(x^5-x)

\int \frac{x - 2}{x ^{5} - x} d x

integral of (2x^{-3}+3x^{-2}+2)

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