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Beliebt Rechnen >

integral of 5xsec^2(3x)

Lösung

\int 5 x sec^{2} (3 x) d x

Lösung

5 (\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 5 x sec^{2} (3 x) d x

Entferne die Konstante:

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

= 5 \cdot \int x sec^{2} (3 x) d x

Umschreiben mit Hilfe von Trigonometrie-Identitäten

= 5 \cdot \int x (1 + tan^{2} (3 x)) d x

Wende die partielle Integration an

= 5 (\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})

= 5 (\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

= 5 (\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 sin^3(5x)cos^4(5x)

\int sin^{3} (5 x) cos^{4} (5 x) d x

integral of (x^2-2x)e^x

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

integral of sqrt(1-2x^2)

\int 1 - 2 x^{2} d x

integral of (sqrt(1+x)-1)/(sqrt(1+x)+1)

\int \frac{1 + x - 1}{1 + x + 1} d x

integral of x(1-7x^2)^6

\int x (1 - 7 x^{2})^{6} d x