integral of 2xsqrt(2x)

Lösung

\int 2 x 2 x d x

2 (\frac{1}{2} x^{2} x - \frac{1}{5 2} x^{\frac{5}{2}}) + C

Schritte zur Lösung

\int 2 x 2 x d x

Entferne die Konstante:

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

= 2 \cdot \int x 2 x d x

Wende die partielle Integration an

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

\int \frac{1}{2 2} x^{\frac{3}{2}} d x = \frac{1}{5 2} x^{\frac{5}{2}}

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

Füge eine Konstante zur Lösung hinzu

= 2 (\frac{1}{2} x^{2} x - \frac{1}{5 2} x^{\frac{5}{2}}) + C

\int \frac{1}{3 x + 2} d x

\int \frac{15}{x ^{2}} d x

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

\int \frac{x}{2} cos (2 x) d x

\int \frac{1}{4} sin (x) d x