integral of tsec^2(4t)

Lösung

\int t sec^{2} (4 t) d t

\frac{1}{2} t^{2} sec^{2} (4 t) - \frac{1}{16} (8 t^{2} tan^{2} (4 t) - 4 t tan (4 t) - ln ∣ cos (4 t) ∣ + 8 t^{2}) + C

Schritte zur Lösung

\int t sec^{2} (4 t) d t

Umschreiben mit Hilfe von Trigonometrie-Identitäten

= \int t (1 + tan^{2} (4 t)) d t

Wende die partielle Integration an

= \frac{1}{2} t^{2} sec^{2} (4 t) - \int 4 t^{2} sec^{2} (4 t) tan (4 t) d t

\int 4 t^{2} sec^{2} (4 t) tan (4 t) d t = \frac{1}{16} (8 t^{2} tan^{2} (4 t) - 4 t tan (4 t) - ln ∣ cos (4 t) ∣ + 8 t^{2})

= \frac{1}{2} t^{2} sec^{2} (4 t) - \frac{1}{16} (8 t^{2} tan^{2} (4 t) - 4 t tan (4 t) - ln ∣ cos (4 t) ∣ + 8 t^{2})

Füge eine Konstante zur Lösung hinzu

= \frac{1}{2} t^{2} sec^{2} (4 t) - \frac{1}{16} (8 t^{2} tan^{2} (4 t) - 4 t tan (4 t) - ln ∣ cos (4 t) ∣ + 8 t^{2}) + C

d er i v a t i v e y = x^{3} (2 x - 1)^{7}

\int x^{8} (x^{9} - 10)^{7} d x

\frac{\partial}{\partial y} (- 5 y z^{4})

\frac{\partial}{\partial x} (\frac{cos ( 2 y )}{e ^{2 x}})

x \to - 3 + lim (f (x))