integral of ((t+1)^2)/(sqrt(t))

Lösung

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

\frac{2}{5} t^{\frac{5}{2}} + \frac{4}{3} t^{\frac{3}{2}} + 2 t + C

Schritte zur Lösung

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

Multipliziere aus

\frac{( t + 1 ) ^{2}}{t} : t^{\frac{3}{2}} + 2 t + \frac{1}{t}

= \int t^{\frac{3}{2}} + 2 t + \frac{1}{t} d t

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int t^{\frac{3}{2}} d t + \int 2 t d t + \int \frac{1}{t} d t

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

\int 2 t d t = \frac{4}{3} t^{\frac{3}{2}}

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

= \frac{2}{5} t^{\frac{5}{2}} + \frac{4}{3} t^{\frac{3}{2}} + 2 t

Füge eine Konstante zur Lösung hinzu

= \frac{2}{5} t^{\frac{5}{2}} + \frac{4}{3} t^{\frac{3}{2}} + 2 t + C