integral of 9x(9-x^{-4})

Lösung

\int 9 x (9 - x^{- 4}) d x

9 (\frac{9 x ^{2}}{2} + \frac{1}{2 x ^{2}}) + C

Schritte zur Lösung

\int 9 x (9 - x^{- 4}) d x

Entferne die Konstante:

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

= 9 \cdot \int x (9 - x^{- 4}) d x

Wende Exponentenregel an:

a^{- b} = \frac{1}{a ^{b}}

= 9 \cdot \int x (9 - \frac{1}{x ^{4}}) d x

Multipliziere aus

x (9 - \frac{1}{x ^{4}}) : 9 x - \frac{1}{x ^{3}}

= 9 \cdot \int 9 x - \frac{1}{x ^{3}} d x

Wende die Summenregel an:

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

= 9 (\int 9 x d x - \int \frac{1}{x ^{3}} d x)

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

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

= 9 (\frac{9 x ^{2}}{2} - (- \frac{1}{2 x ^{2}}))

Vereinfache

= 9 (\frac{9 x ^{2}}{2} + \frac{1}{2 x ^{2}})

Füge eine Konstante zur Lösung hinzu

= 9 (\frac{9 x ^{2}}{2} + \frac{1}{2 x ^{2}}) + C

x \to 3 - lim (\frac{x - 3}{x ^{2} - 9})

t an g e n t y = (x^{3} - 25 x)^{12}, (5, 0)

\int x sin (d) x d x

x \to \frac{π}{4} lim (sec (x))

\frac{d ^{2}}{d x ^{2}} (r + 8 r)