integral of 8xcos^2(x)

Lösung

\int 8 x cos^{2} (x) d x

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

Schritte zur Lösung

\int 8 x cos^{2} (x) d x

Entferne die Konstante:

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

= 8 \cdot \int x cos^{2} (x) d x

Wende die partielle Integration an

= 8 (\frac{1}{2} x (x + \frac{1}{2} sin (2 x)) - \int \frac{1}{2} (x + \frac{1}{2} sin (2 x)) d x)

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

= 8 (\frac{1}{2} x (x + \frac{1}{2} sin (2 x)) - \frac{1}{2} (\frac{x ^{2}}{2} - \frac{1}{4} cos (2 x)))

Füge eine Konstante zur Lösung hinzu

= 8 (\frac{1}{2} x (x + \frac{1}{2} sin (2 x)) - \frac{1}{2} (\frac{x ^{2}}{2} - \frac{1}{4} cos (2 x))) + C

\frac{\partial}{\partial x} ((x - 7)^{2} + (y - 1)^{2} + 29)

x \to 4 lim (\frac{3}{x - 4})

n \to \infty lim (i = 3 \sum 8 (i + 1)^{2})

\int \frac{1}{11 - x ^{2}} d x

\int (\frac{3}{x ^{7}}) d x