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

Lösung

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

2 - 1

Dezimale

0.41421 \dots

Schritte zur Lösung

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

Wende U-Substitution an

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

Wende die Potenzregel an

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

Wende Radikal Regel an:

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

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

Berechne die Grenzen:

22 - 2

= \frac{1}{2} (22 - 2)

Vereinfache

= 2 - 1

\frac{d}{d x} (1 + 2 sin (\frac{x ^{2}}{2}))

\int \frac{4}{x ^{2} + 16} d x

\int \frac{2 ( x + 2 )}{5} d x

t an g e n t f (x) = \frac{x ^{3} + 2}{3}, at x = - 3

\frac{d}{d x} (x^{4} + y^{4})