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Beliebt Rechnen >

integral from 0 to 8 of 1/(x^2+16)

Lösung

\int_{0}^{8} \frac{1}{x ^{2} + 16} d x

Lösung

\frac{1}{4} arctan (2)

+1

Dezimale

0.27678 \dots

Schritte zur Lösung

\int_{0}^{8} \frac{1}{x ^{2} + 16} d x

Wende integrale Substitution an

= \int_{0}^{2} \frac{1}{4 ( u ^{2} + 1 )} d u

Entferne die Konstante:

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

= \frac{1}{4} \cdot \int_{0}^{2} \frac{1}{u ^{2} + 1} d u

Nutze das gemeinsame Integral :

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

= \frac{1}{4} [arctan (u)]_{0}^{2}

Berechne die Grenzen:

arctan (2)

= \frac{1}{4} arctan (2)

Graph

Beliebte Beispiele

f(X)=(ln(2))/(ln(X))

f (X) = \frac{ln ( 2 )}{ln ( X )}

-derivative of (dy/(dx))+400y=0

- \frac{d}{d x} (\frac{d y}{d x}) + 400 y = 0

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\int sin^{9} (x) cos (x) d x

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\int \frac{sin ( π x )}{π} d x

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