integral of x4^x

Lösung

\int x 4^{x} d x

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

Schritte zur Lösung

\int x \cdot 4^{x} d x

Wende die partielle Integration an

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

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

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

Füge eine Konstante zur Lösung hinzu

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

d er i v a t i v e y = (cos (x))^{s i n (x)}

\int \frac{x}{2 x + 1} d x

x \to 2 lim ((3 - x) (x + 1))

\frac{\partial}{\partial x} (\frac{5}{x y} - 4 x^{2} - 2 y^{2})

\int \frac{1}{x ^{2} - 4 x + 8} d x