integral of (1+cos^2(x))

Lösung

\int (1 + cos^{2} (x)) d x

\frac{3}{2} x + \frac{1}{4} sin (2 x) + C

Schritte zur Lösung

\int 1 + cos^{2} (x) d x

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int 1 d x + \int cos^{2} (x) d x

\int 1 d x = x

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

= x + \frac{1}{2} (x + \frac{1}{2} sin (2 x))

Vereinfache

x + \frac{1}{2} (x + \frac{1}{2} sin (2 x)) : \frac{3}{2} x + \frac{1}{4} sin (2 x)

= \frac{3}{2} x + \frac{1}{4} sin (2 x)

Füge eine Konstante zur Lösung hinzu

= \frac{3}{2} x + \frac{1}{4} sin (2 x) + C

x \to \infty lim (5 e^{- t} i - \frac{5 t}{t + 7} j + 5 arctan (t k))

\frac{\partial}{\partial x} (x^{2} + y^{2} + 3 x y + 5 x)

x^{2} y^{^{'}} + (2 - y) = 0

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

\frac{\partial}{\partial x} (7 x y^{3} + 5)