integral from 0 to 1 of (3x-1)^{50}

Lösung

\int_{0}^{1} (3 x - 1)^{50} d x

\frac{2 ^{51} + 1}{153}

Dezimale

1.47176 E 13

Schritte zur Lösung

\int_{0}^{1} (3 x - 1)^{50} d x

Wende U-Substitution an

= \int_{- 1}^{2} \frac{u ^{50}}{3} d u

Entferne die Konstante:

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

= \frac{1}{3} \cdot \int_{- 1}^{2} u^{50} d u

Wende die Potenzregel an

= \frac{1}{3} [\frac{u ^{51}}{51}]_{- 1}^{2}

Berechne die Grenzen:

\frac{2 ^{51}}{51} + \frac{1}{51}

= \frac{1}{3} (\frac{2 ^{51}}{51} + \frac{1}{51})

Vereinfache

= \frac{2 ^{51} + 1}{153}

\int 7 x^{9} e^{- x^{5}} d x

\frac{\partial}{\partial x} (4 e^{x} ln (1 + y))

x \to \infty + lim ((1 + \frac{1}{x})^{\frac{x}{6}})

n = 6 \sum \infty \frac{n}{n ^{2} + 1}

\frac{\partial}{\partial y} (x^{2} y z^{2})