integral of (xsqrt(x)+sqrt(x))/(x^2)

Lösung

\int \frac{x x + x}{x ^{2}} d x

2 x - \frac{2}{x} + C

Schritte zur Lösung

\int \frac{x x + x}{x ^{2}} d x

\frac{x x + x}{x ^{2}} = (\frac{x x}{x ^{2}} + \frac{x}{x ^{2}})

= \int \frac{x x}{x ^{2}} + \frac{x}{x ^{2}} d x

Vereinfache

\frac{x x}{x ^{2}} + \frac{x}{x ^{2}} : \frac{1}{x} + \frac{1}{x ^{\frac{3}{2}}}

= \int \frac{1}{x} + \frac{1}{x ^{\frac{3}{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{1}{x} d x + \int \frac{1}{x ^{\frac{3}{2}}} d x

\int \frac{1}{x} d x = 2 x

\int \frac{1}{x ^{\frac{3}{2}}} d x = - \frac{2}{x}

= 2 x - \frac{2}{x}

Füge eine Konstante zur Lösung hinzu

= 2 x - \frac{2}{x} + C

\int (\frac{3}{x} + \frac{5}{x ^{2}}) d x

l a pl a ce t r an s f or m 3 sin (5 t + 45)

\int \frac{( x ^{7} + 3 x ^{5} - 2 x ^{3} - 4 )}{x ^{3}} d x

\frac{\partial}{\partial y} (1000 - 4 x y + x y^{2})

\frac{\partial}{\partial x} (e^{- 3 t} cos (π x))