integral of (10^x+3e^{2x}+x^{-3})

Lösung

\int (1 0^{x} + 3 e^{2 x} + x^{- 3}) d x

\frac{1 0 ^{x}}{ln ( 10 )} + \frac{3}{2} e^{2 x} - \frac{1}{2 x ^{2}} + C

Schritte zur Lösung

\int 1 0^{x} + 3 e^{2 x} + 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

= \int 1 0^{x} d x + \int 3 e^{2 x} d x + \int x^{- 3} d x

\int 1 0^{x} d x = \frac{1 0 ^{x}}{ln ( 10 )}

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

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

= \frac{1 0 ^{x}}{ln ( 10 )} + \frac{3}{2} e^{2 x} - \frac{1}{2 x ^{2}}

Füge eine Konstante zur Lösung hinzu

= \frac{1 0 ^{x}}{ln ( 10 )} + \frac{3}{2} e^{2 x} - \frac{1}{2 x ^{2}} + C

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