de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

integral of tsec^2(9t)

Lösung

\int t sec^{2} (9 t) d t

Lösung

\frac{1}{2} t^{2} sec^{2} (9 t) - \frac{1}{162} (81 t^{2} tan^{2} (9 t) - 18 t tan (9 t) - 2 ln ∣ cos (9 t) ∣ + 81 t^{2}) + C

Schritte zur Lösung

\int t sec^{2} (9 t) d t

Umschreiben mit Hilfe von Trigonometrie-Identitäten

= \int t (1 + tan^{2} (9 t)) d t

Wende die partielle Integration an

= \frac{1}{2} t^{2} sec^{2} (9 t) - \int 9 t^{2} sec^{2} (9 t) tan (9 t) d t

\int 9 t^{2} sec^{2} (9 t) tan (9 t) d t = \frac{1}{162} (81 t^{2} tan^{2} (9 t) - 18 t tan (9 t) - 2 ln ∣ cos (9 t) ∣ + 81 t^{2})

= \frac{1}{2} t^{2} sec^{2} (9 t) - \frac{1}{162} (81 t^{2} tan^{2} (9 t) - 18 t tan (9 t) - 2 ln ∣ cos (9 t) ∣ + 81 t^{2})

Füge eine Konstante zur Lösung hinzu

= \frac{1}{2} t^{2} sec^{2} (9 t) - \frac{1}{162} (81 t^{2} tan^{2} (9 t) - 18 t tan (9 t) - 2 ln ∣ cos (9 t) ∣ + 81 t^{2}) + C

Graph

Beliebte Beispiele

derivative of-5x^2+10

\frac{d}{d x} (- 5 x^{2} + 10)

derivative of 1/(x^n)

\frac{d}{d x} (\frac{1}{x ^{n}})

derivative y=(4x^2+4x+8)/(sqrt(x))

d er i v a t i v e y = \frac{4 x ^{2} + 4 x + 8}{x}

(\partial)/(\partial x)(y-x^2-7z^2)

\frac{\partial}{\partial x} (y - x^{2} - 7 z^{2})

tangent f(x)=x^2+8,\at x=2

t an g e n t f (x) = x^{2} + 8, at x = 2