integral of x(cos^2(x))

Lösung

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

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

Wende die partielle Integration an

= \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))

= \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

= \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

(x^{2} + 1) y^{^{'}} + 8 x (y - 1) = 0, y (0) = 3

\frac{\partial}{\partial x} (4 x^{2} - 4 x y + x yz)

\int (t^{2} - 1) (4 + 3 t) d t

t an g e n t f (x) = x^{4}, at x = 1

t an g e n t y = \frac{6}{x}, (25, \frac{6}{5})