integral of ((sqrt(x-1))^2)/(sqrt(x))

Lösung

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

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

Schritte zur Lösung

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

(x - 1)^{2} = x - 1

= \int \frac{x - 1}{x} d x

Multipliziere aus

\frac{x - 1}{x} : x - \frac{1}{x}

= \int x - \frac{1}{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{1}{x} d x

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

\int \frac{1}{x} d x = 2 x

= \frac{2}{3} x^{\frac{3}{2}} - 2 x

Füge eine Konstante zur Lösung hinzu

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

\int e^{6 - 5 x} d x

\int 9 x^{2} + 16 d x

\int (\frac{6 + x + x}{x}) d x

\int \frac{arctan ( y )}{1 + y ^{2}} d y

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