integral of (sqrt(x)+3/(sqrt(x)))

Lösung

\int (x + \frac{3}{x}) d x

\frac{2}{3} x^{\frac{3}{2}} + 6 x + C

Schritte zur Lösung

\int x + \frac{3}{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 x d x + \int \frac{3}{x} d x

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

\int \frac{3}{x} d x = 6 x

= \frac{2}{3} x^{\frac{3}{2}} + 6 x

Füge eine Konstante zur Lösung hinzu

= \frac{2}{3} x^{\frac{3}{2}} + 6 x + C

x \to - 1 lim ((1 + x)^{- 1})

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

y^{^{'}} = \frac{t ^{2} + t y + y ^{2}}{t ^{2}}

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

\frac{d y}{d x} + \frac{2 y}{x} = \frac{1}{x ^{2}}