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Beliebt Rechnen >

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

Lösung

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

Lösung

\frac{2}{9}

+1

Dezimale

0.22222 \dots

Schritte zur Lösung

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

Wende U-Substitution an

= \int_{1}^{9} \frac{1}{4 u ^{2}} d u

Entferne die Konstante:

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

= \frac{1}{4} \cdot \int_{1}^{9} \frac{1}{u ^{2}} d u

Wende die Potenzregel an

= \frac{1}{4} [- \frac{1}{u}]_{1}^{9}

Berechne die Grenzen:

\frac{8}{9}

= \frac{1}{4} \cdot \frac{8}{9}

Vereinfache

= \frac{2}{9}

Graph

Beliebte Beispiele

integral from-18 to 32 of 1/(sqrt(2x))

\int_{- 18}^{32} \frac{1}{2 x} d x

(d^2)/(dx^2)(sqrt(x^2+11))

\frac{d ^{2}}{d x ^{2}} (x^{2} + 11)

integral from 0 to 1 of x^2e^{x^3+0}

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

y^{^{''}} + y = x

tangent f(x)=3x^2+3x,\at x=-2

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