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Beliebt Rechnen >

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

Lösung

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

Lösung

\frac{π}{2}

+1

Dezimale

1.57079 \dots

Schritte zur Lösung

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

Wende U-Substitution an

= \int_{0}^{1} \frac{2}{u ^{2} + 1} d u

Entferne die Konstante:

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

= 2 \cdot \int_{0}^{1} \frac{1}{u ^{2} + 1} d u

Nutze das gemeinsame Integral :

\int \frac{1}{u ^{2} + 1} d u = arctan (u)

= 2 [arctan (u)]_{0}^{1}

Berechne die Grenzen:

\frac{π}{4}

= 2 \cdot \frac{π}{4}

Vereinfache

= \frac{π}{2}

Graph

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integral of (1/(x^2+9))

\int (\frac{1}{x ^{2} + 9}) d x

derivative y=((x-5))/(x^3)

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derivative of 1/(2x+2)

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