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Beliebt Rechnen >

integral from 0 to 2 of arctan(x/2)

Lösung

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

Lösung

\frac{π}{2} - ln (2)

+1

Dezimale

0.87764 \dots

Schritte zur Lösung

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

Wende die partielle Integration an

= [x arctan (\frac{x}{2}) - \int \frac{2 x}{x ^{2} + 4} d x]_{0}^{2}

\int \frac{2 x}{x ^{2} + 4} d x = ln x^{2} + 4

= [x arctan (\frac{x}{2}) - ln x^{2} + 4]_{0}^{2}

Berechne die Grenzen:

\frac{π}{2} - ln (2)

= \frac{π}{2} - ln (2)

Graph

Beliebte Beispiele

integral of (10)/(1+x^2)

\int \frac{10}{1 + x ^{2}} d x

limit as x approaches 0 of (arcsin(2x)-2arcsin(x))/(x^3)

x \to 0 lim (\frac{arcsin ( 2 x ) - 2 arcsin ( x )}{x ^{3}})

tangent f(x)=x^2

t an g e n t f (x) = x^{2}

2x^2y(dy)/(dx)+1+2xy^2=0

2 x^{2} y \frac{d y}{d x} + 1 + 2 x y^{2} = 0

(\partial}{\partial x}(xy+\frac{27)/x)

\frac{\partial}{\partial x} (x y + \frac{27}{x})