integral of (3x-x^{-1})^2

Lösung

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

3 x^{3} - 6 x - \frac{1}{x} + C

Schritte zur Lösung

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

Vereinfache

(3 x - x^{- 1})^{2} : 9 x^{2} - 6 + \frac{1}{x ^{2}}

= \int 9 x^{2} - 6 + \frac{1}{x ^{2}} 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

= \int 9 x^{2} d x - \int 6 d x + \int \frac{1}{x ^{2}} d x

\int 9 x^{2} d x = 3 x^{3}

\int 6 d x = 6 x

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

= 3 x^{3} - 6 x - \frac{1}{x}

Füge eine Konstante zur Lösung hinzu

= 3 x^{3} - 6 x - \frac{1}{x} + C

\frac{d}{d x} (\frac{x}{x ^{2} + a ^{2}})

\int \frac{1}{e ^{3 y}} d y

f (r) = 2 π r^{2}

\frac{d}{d x} (sin (2 π (1 - x)))

\int \frac{cos ( t )}{7 + sin ( t )} d t