integral of (2/(x^3)+3/(x^2)+3^x)

Lösung

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

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

Schritte zur Lösung

\int \frac{2}{x ^{3}} + \frac{3}{x ^{2}} + 3^{x} 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 \frac{2}{x ^{3}} d x + \int \frac{3}{x ^{2}} d x + \int 3^{x} d x

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

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

\int 3^{x} d x = \frac{3 ^{x}}{ln ( 3 )}

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

Füge eine Konstante zur Lösung hinzu

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

\int \frac{6 x ^{5}}{( x ^{6} - 1 ) ^{2}} d x

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

\int \frac{3 - e ^{x}}{e ^{7 x}} d x

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

\int 9 - 16 y^{2} d y