integral of ((x+1)/(\sqrt[4]{x)})

Lösung

\int (\frac{x + 1}{4 x}) d x

\frac{4}{7} x^{\frac{7}{4}} + \frac{4}{3} x^{\frac{3}{4}} + C

Schritte zur Lösung

\int \frac{x + 1}{4 x} d x

Multipliziere aus

\frac{x + 1}{4 x} : x^{\frac{3}{4}} + \frac{1}{4 x}

= \int x^{\frac{3}{4}} + \frac{1}{4 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^{\frac{3}{4}} d x + \int \frac{1}{4 x} d x

\int x^{\frac{3}{4}} d x = \frac{4}{7} x^{\frac{7}{4}}

\int \frac{1}{4 x} d x = \frac{4}{3} x^{\frac{3}{4}}

= \frac{4}{7} x^{\frac{7}{4}} + \frac{4}{3} x^{\frac{3}{4}}

Füge eine Konstante zur Lösung hinzu

= \frac{4}{7} x^{\frac{7}{4}} + \frac{4}{3} x^{\frac{3}{4}} + C

y^{2} d y + x^{2} d x = 0

d er i v a t i v e \frac{7}{3} x^{3} (4 x^{5} - 11)^{3}

d er i v a t i v e - 8 x y

\frac{\partial}{\partial x} (x^{2} y^{2} - 3 x)

s l o p e (- 7, - 4), (- 11, - 2)