integral of ((sqrt(5x))/5+5/(sqrt(5x)))

Lösung

\int (\frac{5 x}{5} + \frac{5}{5 x}) d x

\frac{2}{3 5} x^{\frac{3}{2}} + 25 x + C

Schritte zur Lösung

\int \frac{5 x}{5} + \frac{5}{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 \frac{5 x}{5} d x + \int \frac{5}{5 x} d x

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

\int \frac{5}{5 x} d x = 25 x

= \frac{2}{3 5} x^{\frac{3}{2}} + 25 x

Füge eine Konstante zur Lösung hinzu

= \frac{2}{3 5} x^{\frac{3}{2}} + 25 x + C

y^{^{''}} + y^{^{'}} - 12 y = 3 e^{2 x}

y^{^{''}} + 6 y^{^{'}} + 8 y = - 6 t e^{4 t}

\int_{1}^{2} \frac{1}{x ( x - 5 )} d x

\int \frac{1}{x 2 + 9 x ^{2}} d x

\frac{d}{d x} (4 x^{\frac{3}{4}})