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Beliebt Rechnen >

integral from 1 to 5 of 4/(x^2+2x+1)

Lösung

\int_{1}^{5} \frac{4}{x ^{2} + 2 x + 1} d x

Lösung

\frac{4}{3}

+1

Dezimale

1.33333 \dots

Schritte zur Lösung

\int_{1}^{5} \frac{4}{x ^{2} + 2 x + 1} d x

Entferne die Konstante:

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

= 4 \cdot \int_{1}^{5} \frac{1}{x ^{2} + 2 x + 1} d x

Vervollständige das Quadrat

x^{2} + 2 x + 1 : (x + 1)^{2}

= 4 \cdot \int_{1}^{5} \frac{1}{( x + 1 ) ^{2}} d x

Wende U-Substitution an

= 4 \cdot \int_{2}^{6} \frac{1}{u ^{2}} d u

Wende die Potenzregel an

= 4 [- \frac{1}{u}]_{2}^{6}

Berechne die Grenzen:

\frac{1}{3}

= 4 \cdot \frac{1}{3}

Vereinfache

= \frac{4}{3}

Graph

Beliebte Beispiele

integral of (sin(x))/(cos^3(x))

\int \frac{sin ( x )}{cos ^{3} ( x )} d x

derivative of-1/((1-x^2))

\frac{d}{d x} (- \frac{1}{( 1 - x ) ^{2}})

derivative y=arctan(sqrt(4t))

d er i v a t i v e y = arctan (4 t)

limit as x approaches 2+of (4x)/(x-2)

x \to 2 + lim (\frac{4 x}{x - 2})

xy^'-2y=x^2-2x-1

x y^{^{'}} - 2 y = x^{2} - 2 x - 1