integral from-infinity to-1 of x/(x^4+1)

Lösung

\int_{- \infty}^{- 1} \frac{x}{x ^{4} + 1} d x

- \frac{π}{8}

Dezimale

- 0.39269 \dots

Schritte zur Lösung

\int_{- \infty}^{- 1} \frac{x}{x ^{4} + 1} d x

Berechne das unbestimmte Integral:

\int \frac{x}{x ^{4} + 1} d x = \frac{1}{2} arctan (x^{2}) + C

Berechne die Grenzen:

\int_{- \infty}^{- 1} \frac{x}{x ^{4} + 1} d x = \frac{π}{8} - \frac{π}{4}

= \frac{π}{8} - \frac{π}{4}

Vereinfache

= - \frac{π}{8}

\int_{12}^{28} x - 3 d x

\int_{0}^{3} (x^{2} + 2 x) d x

\int_{0}^{\frac{π}{4}} (cos (x))^{2} d x

\int_{- 2 π}^{2 π} \frac{π - x}{2} d x

\int_{4}^{6} \frac{2}{( x - 3 ) ^{2}} d x