integral of 3(t+1)^{1/2}

Lösung

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

2 t (t + 1)^{\frac{1}{2}} + 2 (t + 1)^{\frac{1}{2}} + C

Schritte zur Lösung

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

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

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

Wende die partielle Integration an

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

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

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

Vereinfache

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

= 2 t (t + 1)^{\frac{1}{2}} + 2 (t + 1)^{\frac{1}{2}}

Füge eine Konstante zur Lösung hinzu

= 2 t (t + 1)^{\frac{1}{2}} + 2 (t + 1)^{\frac{1}{2}} + C

x \to 0.5 lim (3 x^{2} + 2 x - 3)

\frac{\partial}{\partial x} (x^{\frac{1}{3}} y^{\frac{2}{3}})

a re a x^{2}, - x^{2} + 4 x

\int \frac{1}{2 - 5 x} d x

x \to 0 lim (x (x - 1))