integral of (8x^2+3x^{-2})

Lösung

\int (8 x^{2} + 3 x^{- 2}) d x

\frac{8 x ^{3}}{3} - \frac{3}{x} + C

Schritte zur Lösung

\int 8 x^{2} + 3 x^{- 2} d x

3 x^{- 2} = \frac{3}{x ^{2}}

= \int 8 x^{2} + \frac{3}{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 8 x^{2} d x + \int \frac{3}{x ^{2}} d x

\int 8 x^{2} d x = \frac{8 x ^{3}}{3}

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

= \frac{8 x ^{3}}{3} - \frac{3}{x}

Füge eine Konstante zur Lösung hinzu

= \frac{8 x ^{3}}{3} - \frac{3}{x} + C

\int \frac{10}{cos ( x ) - 1} d x

\frac{\partial}{\partial x} (\frac{1}{( x + y )})

\int 4 t^{4} e^{6 t^{5}} d t

n \to \infty lim ((1)^{n})

\frac{d y}{d x} (x + y) = x - y