integral of (3x^2)/5+(7x^3)/8

Lösung

\int \frac{3 x ^{2}}{5} + \frac{7 x ^{3}}{8} d x

\frac{x ^{3}}{5} + \frac{7 x ^{4}}{32} + C

Schritte zur Lösung

\int \frac{3 x ^{2}}{5} + \frac{7 x ^{3}}{8} 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{3 x ^{2}}{5} d x + \int \frac{7 x ^{3}}{8} d x

\int \frac{3 x ^{2}}{5} d x = \frac{x ^{3}}{5}

\int \frac{7 x ^{3}}{8} d x = \frac{7 x ^{4}}{32}

= \frac{x ^{3}}{5} + \frac{7 x ^{4}}{32}

Füge eine Konstante zur Lösung hinzu

= \frac{x ^{3}}{5} + \frac{7 x ^{4}}{32} + C

\int - 10 x^{5} e^{x^{6}} d x

\int \frac{3}{x ( x + 1 )} d x

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

\int (\frac{3}{x} - \frac{10}{x ^{6}}) d x

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