integral from 0 to 1 of x^2(2+2x^3)^3

Lösung

\int_{0}^{1} x^{2} (2 + 2 x^{3})^{3} d x

10

Schritte zur Lösung

\int_{0}^{1} x^{2} (2 + 2 x^{3})^{3} d x

Wende U-Substitution an

= \int_{2}^{4} \frac{u ^{3}}{6} d u

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{6} \cdot \int_{2}^{4} u^{3} d u

Wende die Potenzregel an

= \frac{1}{6} [\frac{u ^{4}}{4}]_{2}^{4}

Berechne die Grenzen:

60

= \frac{1}{6} \cdot 60

Vereinfache

= 10

\int_{- 3}^{2} - x^{2} - x + 6 d x

\int_{- 3}^{3} - x^{2} + 9 d x

\int_{a}^{b} \frac{1}{( x - a ) ^{n}} d x

\int_{- 1}^{2} (4 x^{2} - 1) (6 x + 3) d x

\int_{0}^{x} arctan (t) d t