integral of tsin^2(t)

Lösung

\int t sin^{2} (t) d t

\frac{1}{2} t (t - \frac{1}{2} sin (2 t)) - \frac{1}{2} (\frac{t ^{2}}{2} + \frac{1}{4} cos (2 t)) + C

Schritte zur Lösung

\int t sin^{2} (t) d t

Wende die partielle Integration an

= \frac{1}{2} t (t - \frac{1}{2} sin (2 t)) - \int \frac{1}{2} (t - \frac{1}{2} sin (2 t)) d t

\int \frac{1}{2} (t - \frac{1}{2} sin (2 t)) d t = \frac{1}{2} (\frac{t ^{2}}{2} + \frac{1}{4} cos (2 t))

= \frac{1}{2} t (t - \frac{1}{2} sin (2 t)) - \frac{1}{2} (\frac{t ^{2}}{2} + \frac{1}{4} cos (2 t))

Füge eine Konstante zur Lösung hinzu

= \frac{1}{2} t (t - \frac{1}{2} sin (2 t)) - \frac{1}{2} (\frac{t ^{2}}{2} + \frac{1}{4} cos (2 t)) + C

x \to 0 lim (3 x^{2} - 5)

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

x \to - 5 lim (2 (- \frac{3}{10}) (x) - 3)

\frac{\partial}{\partial y} (cos (x + y + z))

\frac{d}{d x} (\frac{e ^{2 x}}{1 + e ^{2 x}})