integral of 2^xx^2

Lösung

\int 2^{x} x^{2} d x

\frac{2 ^{x} x ^{2}}{ln ( 2 )} - \frac{1}{ln ( 2 )} (\frac{2 ^{x + 1} x}{ln ( 2 )} - \frac{1}{ln ^{2} ( 2 )} \cdot 2^{1 + x}) + C

Schritte zur Lösung

\int 2^{x} x^{2} d x

Wende die partielle Integration an

= \frac{2 ^{x} x ^{2}}{ln ( 2 )} - \int \frac{2 ^{x + 1} x}{ln ( 2 )} d x

\int \frac{2 ^{x + 1} x}{ln ( 2 )} d x = \frac{1}{ln ( 2 )} (\frac{2 ^{x + 1} x}{ln ( 2 )} - \frac{1}{ln ^{2} ( 2 )} \cdot 2^{1 + x})

= \frac{2 ^{x} x ^{2}}{ln ( 2 )} - \frac{1}{ln ( 2 )} (\frac{2 ^{x + 1} x}{ln ( 2 )} - \frac{1}{ln ^{2} ( 2 )} \cdot 2^{1 + x})

Füge eine Konstante zur Lösung hinzu

= \frac{2 ^{x} x ^{2}}{ln ( 2 )} - \frac{1}{ln ( 2 )} (\frac{2 ^{x + 1} x}{ln ( 2 )} - \frac{1}{ln ^{2} ( 2 )} \cdot 2^{1 + x}) + C

\int x^{5} x^{6} + 3 d x

y^{^{'}} + y = t e^{- t} + e^{t}

x \to 0 lim (ln (\frac{x}{x - 1}))

in v erse l a pl a ce \frac{e ^{- s}}{s - 8}

\int 4 - 2 x d x