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

Lösung

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

\frac{3}{16}

Dezimale

0.1875

Schritte zur Lösung

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

Wende U-Substitution an

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

Wende die Potenzregel an

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

Berechne die Grenzen:

\frac{3}{8}

= \frac{1}{2} \cdot \frac{3}{8}

Vereinfache

= \frac{3}{16}

\int_{- 2}^{0} π (2 x^{2} + 4 x + 3)^{2} d x

\frac{d}{d x} (cos^{2} (x^{2} + 3))

\frac{\partial}{\partial y} (y - e^{t})

csc (y) d x + sec (2 x) d y = 0

\frac{\partial}{\partial x} (cos (π) x)