integral of (3x-1)sqrt(x+6)

Lösung

\int (3 x - 1) x + 6 d x

2 x (x + 6)^{\frac{3}{2}} - \frac{2}{3} (x + 6)^{\frac{3}{2}} - \frac{4}{5} (x + 6)^{\frac{5}{2}} + C

Schritte zur Lösung

\int (3 x - 1) x + 6 d x

Wende die partielle Integration an

= 2 x (x + 6)^{\frac{3}{2}} - \frac{2}{3} (x + 6)^{\frac{3}{2}} - \int 2 (x + 6)^{\frac{3}{2}} d x

\int 2 (x + 6)^{\frac{3}{2}} d x = \frac{4}{5} (x + 6)^{\frac{5}{2}}

= 2 x (x + 6)^{\frac{3}{2}} - \frac{2}{3} (x + 6)^{\frac{3}{2}} - \frac{4}{5} (x + 6)^{\frac{5}{2}}

Füge eine Konstante zur Lösung hinzu

= 2 x (x + 6)^{\frac{3}{2}} - \frac{2}{3} (x + 6)^{\frac{3}{2}} - \frac{4}{5} (x + 6)^{\frac{5}{2}} + C

d er i v a t i v e ln (\frac{2 x + 1}{x ^{2} - 4})

in v erse l a pl a ce \frac{1}{s ^{2} ( s ^{2} + 1 ) ^{2}}

x \to 0 + lim ((1 + 4 x)^{c o t (x)})

t a y l or x^{2} + 1

y^{^{'}} = 2 y + 39