integral of (4sin(x)+(2x^5-sqrt(x))/x)

Lösung

\int (4 sin (x) + \frac{2 x ^{5} - x}{x}) d x

- 4 cos (x) + \frac{2 x ^{5}}{5} - 2 x + C

Schritte zur Lösung

\int 4 sin (x) + \frac{2 x ^{5} - 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 4 sin (x) d x + \int \frac{2 x ^{5} - x}{x} d x

\int 4 sin (x) d x = - 4 cos (x)

\int \frac{2 x ^{5} - x}{x} d x = \frac{2 x ^{5}}{5} - 2 x

= - 4 cos (x) + \frac{2 x ^{5}}{5} - 2 x

Füge eine Konstante zur Lösung hinzu

= - 4 cos (x) + \frac{2 x ^{5}}{5} - 2 x + C

d er i v a t i v e f (x) = \frac{4 x ^{\frac{3}{2}}}{x}

\frac{d}{d x} (cos (5 x - 9))

in v erse l a pl a ce \frac{2 s}{s ^{2} + s}

d er i v a t i v e y = 3 e^{4 x}

\int 6 x^{2} \cdot e^{x^{3}} d x