integral of (1-cos(x))/x

Lösung

\int \frac{1 - cos ( x )}{x} d x

ln ∣ x ∣ - Ci (x) + C

Schritte zur Lösung

\int \frac{1 - cos ( x )}{x} d x

Multipliziere aus

\frac{1 - cos ( x )}{x} : \frac{1}{x} - \frac{cos ( x )}{x}

= \int \frac{1}{x} - \frac{cos ( x )}{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 \frac{1}{x} d x - \int \frac{cos ( x )}{x} d x

\int \frac{1}{x} d x = ln ∣ x ∣

\int \frac{cos ( x )}{x} d x = Ci (x)

= ln ∣ x ∣ - Ci (x)

Füge eine Konstante zur Lösung hinzu

= ln ∣ x ∣ - Ci (x) + C

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

\int x - \frac{e ^{x}}{y ^{2}} - 2 y d y

t a y l or x^{\frac{11}{2}}, 1.2

\int \frac{1}{1 - 8 x} d x

t an g e n t f (x) = \frac{9 x}{( x + 1 ) ^{2}}, (0, 0)