integral of x(2^x)

Lösung

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

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

Schritte zur Lösung

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

Wende die partielle Integration an

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

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

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

Füge eine Konstante zur Lösung hinzu

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

\int 30 sin (4 x - 2) cos (x + 1) d x

\int e^{(x^{3} - 6 x)} (x^{2} - 2) d x

\int (2 x^{5} - x^{2})^{2} (x^{- \frac{1}{2}}) d x

\int (- 5 x + 1) d x

\int \frac{4 y}{x ^{3}} d x