integral of 2^x-1-(3x)/2

Lösung

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

\frac{2 ^{x}}{ln ( 2 )} - x - \frac{3 x ^{2}}{4} + C

Schritte zur Lösung

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

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

\int 1 d x = x

\int \frac{3 x}{2} d x = \frac{3 x ^{2}}{4}

= \frac{2 ^{x}}{ln ( 2 )} - x - \frac{3 x ^{2}}{4}

Füge eine Konstante zur Lösung hinzu

= \frac{2 ^{x}}{ln ( 2 )} - x - \frac{3 x ^{2}}{4} + C

\int \frac{1}{( x ^{2} - a ^{2} ) ^{3}} d x

\int - 0.08 x^{2} + 4 x d x

\int x^{2} (4 - x^{3})^{4} d x

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

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