integral from 0 to 1 of x^4(1+2x^5)^3

Lösung

\int_{0}^{1} x^{4} (1 + 2 x^{5})^{3} d x

2

Schritte zur Lösung

\int_{0}^{1} x^{4} (1 + 2 x^{5})^{3} d x

Wende U-Substitution an

= \int_{1}^{3} \frac{u ^{3}}{10} d u

Entferne die Konstante:

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

= \frac{1}{10} \cdot \int_{1}^{3} u^{3} d u

Wende die Potenzregel an

= \frac{1}{10} [\frac{u ^{4}}{4}]_{1}^{3}

Berechne die Grenzen:

20

= \frac{1}{10} \cdot 20

Vereinfache

= 2

\int_{0}^{2} x^{2} - x d x

\int_{- 2}^{- 1} \frac{1}{x x ^{2} - 1} d x

\int_{- 1}^{1} t^{2} d t

\int_{0}^{1} a x + b x^{2} d x

\int_{- 1}^{1} - 1 - x^{2} d x