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

Lösung

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

\frac{x ^{4}}{4} + \frac{x ^{5}}{5} + C

Schritte zur Lösung

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

Multipliziere aus

(x^{2} + x^{3}) x : x^{3} + x^{4}

= \int x^{3} + x^{4} 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 x^{3} d x + \int x^{4} d x

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

\int x^{4} d x = \frac{x ^{5}}{5}

= \frac{x ^{4}}{4} + \frac{x ^{5}}{5}

Füge eine Konstante zur Lösung hinzu

= \frac{x ^{4}}{4} + \frac{x ^{5}}{5} + C

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

\int \frac{1}{z ^{3}} d z

\int arcsin (x) arccos (x) d x

\int \frac{4 t ^{2} + 3 t - 1}{t ^{3} - t ^{2}} d t

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