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

Lösung

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

\frac{x ^{2}}{y} + \frac{x ^{3}}{y ^{2}} + C

Schritte zur Lösung

\int 3 x^{2} y^{- 2} + 2 x y^{- 1} 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 2 y^{- 1} x d x + \int 3 y^{- 2} x^{2} d x

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

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

= \frac{x ^{2}}{y} + \frac{x ^{3}}{y ^{2}}

Füge eine Konstante zur Lösung hinzu

= \frac{x ^{2}}{y} + \frac{x ^{3}}{y ^{2}} + C

\frac{d}{d x} (\frac{( x + 1 ) ( 3 x - 7 )}{3 x + 1})

\int_{- 2}^{2} (x^{2} - 2)^{2} d x

\frac{d}{d x} (1 - (1 - 0.01 x)^{3})

\frac{d}{d x} (2^{3 x - 2 x^{2}})

d er i v a t i v e f (x) = 1 - \frac{1}{x}