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Beliebt Rechnen >

integral from-3 to 3 of 1/(x^2+9)

Lösung

\int_{- 3}^{3} \frac{1}{x ^{2} + 9} d x

Lösung

\frac{π}{6}

+1

Dezimale

0.52359 \dots

Schritte zur Lösung

\int_{- 3}^{3} \frac{1}{x ^{2} + 9} d x

Wende integrale Substitution an

= \int_{- 1}^{1} \frac{1}{3 ( u ^{2} + 1 )} d u

Entferne die Konstante:

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

= \frac{1}{3} \cdot \int_{- 1}^{1} \frac{1}{u ^{2} + 1} d u

Nutze das gemeinsame Integral :

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

= \frac{1}{3} [arctan (u)]_{- 1}^{1}

Berechne die Grenzen:

\frac{π}{2}

= \frac{1}{3} \cdot \frac{π}{2}

Vereinfache

= \frac{π}{6}

Graph

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derivative 10cos(t)

d er i v a t i v e 10 cos (t)

derivative of (3x-1^4(7x^2-4)^{-3})

\frac{d}{d x} ((3 x - 1)^{4} (7 x^{2} - 4)^{- 3})

integral of 4x(3x-1)^5

\int 4 x (3 x - 1)^{5} d x

tangent x^2+2xy-y^2+x=20,(3,4)

t an g e n t x^{2} + 2 x y - y^{2} + x = 20, (3, 4)

tangent (3x+6)^{1/5},\at x=2

t an g e n t (3 x + 6)^{\frac{1}{5}}, at x = 2