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Beliebt Rechnen >

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

Lösung

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

Lösung

\frac{π}{2}

+1

Dezimale

1.57079 \dots

Schritte zur Lösung

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

Wende U-Substitution an

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

Nutze das gemeinsame Integral :

\int \frac{1}{1 + u ^{2}} 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

Beliebte Beispiele

integral of ysqrt(y+1)

\int y y + 1 d y

derivative 4tan^2(3x)

d er i v a t i v e 4 tan^{2} (3 x)

integral of-ln(x)

\int - ln (x) d x

(\partial)/(\partial y)(1/(x^2+y^2))

\frac{\partial}{\partial y} (\frac{1}{x ^{2} + y ^{2}})

limit as n approaches infinity of an

n \to \infty lim (an)