integral from-infinity to infinity of 1/(x^2+6x+109)

Lösung

\int_{- \infty}^{\infty} \frac{1}{x ^{2} + 6 x + 109} d x

\frac{π}{10}

Dezimale

0.31415 \dots

Schritte zur Lösung

\int_{- \infty}^{\infty} \frac{1}{x ^{2} + 6 x + 109} d x

Berechne das unbestimmte Integral:

\int \frac{1}{x ^{2} + 6 x + 109} d x = \frac{1}{10} arctan (\frac{x + 3}{10}) + C

Berechne die Grenzen:

\int_{- \infty}^{\infty} \frac{1}{x ^{2} + 6 x + 109} d x = \frac{π}{20} - (- \frac{π}{20})

= \frac{π}{20} - (- \frac{π}{20})

Vereinfache

= \frac{π}{10}

\int_{0}^{1} \frac{x e ^{x}}{( 1 + x ) ^{2}} d x

\int_{- 1}^{1} x^{2} d x

\int_{0}^{1} (2 - x) e^{x} d x

\int_{0}^{1} \frac{4 x}{3} + y^{2} d y

\int_{- 1}^{5} 1 d x