integral of (4x+3)sqrt(1+2x)

Lösung

\int (4 x + 3) 1 + 2 x d x

\frac{4}{3} x (1 + 2 x)^{\frac{3}{2}} + (1 + 2 x)^{\frac{3}{2}} - \frac{4}{15} (1 + 2 x)^{\frac{5}{2}} + C

Schritte zur Lösung

\int (4 x + 3) 1 + 2 x d x

Wende die partielle Integration an

= \frac{4}{3} x (1 + 2 x)^{\frac{3}{2}} + (1 + 2 x)^{\frac{3}{2}} - \int \frac{4}{3} (1 + 2 x)^{\frac{3}{2}} d x

\int \frac{4}{3} (1 + 2 x)^{\frac{3}{2}} d x = \frac{4}{15} (1 + 2 x)^{\frac{5}{2}}

= \frac{4}{3} x (1 + 2 x)^{\frac{3}{2}} + (1 + 2 x)^{\frac{3}{2}} - \frac{4}{15} (1 + 2 x)^{\frac{5}{2}}

Füge eine Konstante zur Lösung hinzu

= \frac{4}{3} x (1 + 2 x)^{\frac{3}{2}} + (1 + 2 x)^{\frac{3}{2}} - \frac{4}{15} (1 + 2 x)^{\frac{5}{2}} + C

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