integral of ((x+4)/(sqrt(x)))

Lösung

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

\frac{2}{3} x^{\frac{3}{2}} + 8 x + C

Schritte zur Lösung

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

Multipliziere aus

\frac{x + 4}{x} : x + \frac{4}{x}

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

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

\int \frac{4}{x} d x = 8 x

= \frac{2}{3} x^{\frac{3}{2}} + 8 x

Füge eine Konstante zur Lösung hinzu

= \frac{2}{3} x^{\frac{3}{2}} + 8 x + C

\frac{\partial}{\partial x} (4 x^{\frac{1}{2}} + y)

\int \frac{( x ^{2} - 3 x + 2 )}{x + 1} d x

\int_{- \infty}^{0} \frac{1}{3 - 7 x} d x

\int sin (2 x) sin (x) d x

\int sec (x) - tan (x) d x