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

Lösung

\int \frac{cos ( x ) - \frac{s i n ( x )}{x}}{x} d x

\frac{sin ( x )}{x} + C

Schritte zur Lösung

\int \frac{cos ( x ) - \frac{s i n ( x )}{x}}{x} d x

Vereinfache

\frac{cos ( x ) - \frac{s i n ( x )}{x}}{x} : \frac{x cos ( x ) - sin ( x )}{x ^{2}}

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

Multipliziere aus

\frac{x cos ( x ) - sin ( x )}{x ^{2}} : \frac{cos ( x )}{x} - \frac{sin ( x )}{x ^{2}}

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

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

\int \frac{sin ( x )}{x ^{2}} d x = - \frac{sin ( x )}{x} + Ci (x)

= Ci (x) - (- \frac{sin ( x )}{x} + Ci (x))

Vereinfache

= \frac{sin ( x )}{x}

Füge eine Konstante zur Lösung hinzu

= \frac{sin ( x )}{x} + C

\frac{\partial}{\partial x} (- 2 x y (6 - x - y))

x \to 0 lim (lo g_{3} (x))

d er i v a t i v e 4 x + 1

\int \frac{2 x - 3}{( x ^{2} - 3 x + 6 ) ^{2}} d x

x \to 4 lim (\frac{x}{x ^{2} + 4})