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

Lösung

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

10 - 1

Dezimale

2.16227 \dots

Schritte zur Lösung

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

Wende U-Substitution an

= \int_{1}^{10} \frac{1}{2 u} d u

Entferne die Konstante:

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

= \frac{1}{2} \cdot \int_{1}^{10} \frac{1}{u} d u

Wende die Potenzregel an

= \frac{1}{2} [2 u^{\frac{1}{2}}]_{1}^{10}

Wende Radikal Regel an:

a^{\frac{1}{n}} = n a

= \frac{1}{2} [2 u]_{1}^{10}

Berechne die Grenzen:

210 - 2

= \frac{1}{2} (210 - 2)

Vereinfache

= 10 - 1

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

\int_{0}^{5} (25 - x^{2}) d x

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

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

\int_{e^{- 1}}^{e^{1}} ∣ ln (x) ∣ d x