integral of (-3x^{-2.5}-7x^{-1})

Lösung

\int (- 3 x^{- 2.5} - 7 x^{- 1}) d x

\frac{2}{x ^{1.5}} - 7 ln ∣ x ∣ + C

Schritte zur Lösung

\int - 3 x^{- 2.5} - 7 x^{- 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 3 x^{- 2.5} d x - \int 7 x^{- 1} d x

\int 3 x^{- 2.5} d x = - \frac{2}{x ^{1.5}}

\int 7 x^{- 1} d x = 7 ln ∣ x ∣

= - (- \frac{2}{x ^{1.5}}) - 7 ln ∣ x ∣

Vereinfache

= \frac{2}{x ^{1.5}} - 7 ln ∣ x ∣

Füge eine Konstante zur Lösung hinzu

= \frac{2}{x ^{1.5}} - 7 ln ∣ x ∣ + C

\frac{d}{d a} (\frac{sin ( a ) + cos ( a )}{sec ( a ) + csc ( a )})

\frac{d}{d x} (10 sin (2 x))

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