integral of (3x^2+4x+5)/(sqrt(x))

Lösung

\int \frac{3 x ^{2} + 4 x + 5}{x} d x

\frac{6}{5} x^{\frac{5}{2}} + \frac{8}{3} x^{\frac{3}{2}} + 10 x + C

Schritte zur Lösung

\int \frac{3 x ^{2} + 4 x + 5}{x} d x

Multipliziere aus

\frac{3 x ^{2} + 4 x + 5}{x} : 3 x^{\frac{3}{2}} + 4 x + \frac{5}{x}

= \int 3 x^{\frac{3}{2}} + 4 x + \frac{5}{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 3 x^{\frac{3}{2}} d x + \int 4 x d x + \int \frac{5}{x} d x

\int 3 x^{\frac{3}{2}} d x = \frac{6}{5} x^{\frac{5}{2}}

\int 4 x d x = \frac{8}{3} x^{\frac{3}{2}}

\int \frac{5}{x} d x = 10 x

= \frac{6}{5} x^{\frac{5}{2}} + \frac{8}{3} x^{\frac{3}{2}} + 10 x

Füge eine Konstante zur Lösung hinzu

= \frac{6}{5} x^{\frac{5}{2}} + \frac{8}{3} x^{\frac{3}{2}} + 10 x + C

\frac{\partial}{\partial y} (16 - 4 x^{2} - y^{2})

d er i v a t i v e g (x) = x^{2} (1 - 5 x)

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

x \to - 8 + lim (\frac{x}{x + 8})

\frac{\partial}{\partial x} (6 x^{3} y + 6 y^{5} + 1)