integral from-3 to 0 of ln(y^2+5)

Lösung

\int_{- 3}^{0} ln (y^{2} + 5) d y

- 6 + 3 ln (14) + 25 arctan (\frac{3}{5})

Dezimale

6.07748 \dots

Schritte zur Lösung

\int_{- 3}^{0} ln (y^{2} + 5) d y

Wende die partielle Integration an

= [y ln (y^{2} + 5) - \int \frac{2 y ^{2}}{y ^{2} + 5} d y]_{- 3}^{0}

\int \frac{2 y ^{2}}{y ^{2} + 5} d y = - 25 arctan (\frac{y}{5}) + 2 y

= [y ln (y^{2} + 5) - (- 25 arctan (\frac{y}{5}) + 2 y)]_{- 3}^{0}

Vereinfache

= [y ln (y^{2} + 5) + 25 arctan (\frac{y}{5}) - 2 y]_{- 3}^{0}

Berechne die Grenzen:

- 6 + 3 ln (14) + 25 arctan (\frac{3}{5})

= - 6 + 3 ln (14) + 25 arctan (\frac{3}{5})

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