integral of (sqrt(n)+3)^3

Lösung

\int (n + 3)^{3} d n

\frac{2}{5} n^{\frac{5}{2}} + \frac{9 n ^{2}}{2} + 18 n^{\frac{3}{2}} + 27 n + C

Schritte zur Lösung

\int (n + 3)^{3} d n

Multipliziere aus

(n + 3)^{3} : n^{\frac{3}{2}} + 9 n + 27 n + 27

= \int n^{\frac{3}{2}} + 9 n + 27 n + 27 d n

Wende die Summenregel an:

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

= \int n^{\frac{3}{2}} d n + \int 9 n d n + \int 27 n d n + \int 27 d n

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

\int 9 n d n = \frac{9 n ^{2}}{2}

\int 27 n d n = 18 n^{\frac{3}{2}}

\int 27 d n = 27 n

= \frac{2}{5} n^{\frac{5}{2}} + \frac{9 n ^{2}}{2} + 18 n^{\frac{3}{2}} + 27 n

Füge eine Konstante zur Lösung hinzu

= \frac{2}{5} n^{\frac{5}{2}} + \frac{9 n ^{2}}{2} + 18 n^{\frac{3}{2}} + 27 n + C

t an g e n t y^{3} = 126 - x^{3}, at x = 5

y^{^{''}} - 12 y^{^{'}} + 100 y = 0

y^{^{'}} = 5 y + e^{- 2 x} y^{- 2}, y (0) = 2

d er i v a t i v e f (x) = x^{10} e^{x}

d er i v a t i v e 3^{(x^{5})}