integral from 1 to 2 of ln(1+x)

Lösung

\int_{1}^{2} ln (1 + x) d x

3 ln (3) - 1 - 2 ln (2)

Dezimale

0.90954 \dots

Schritte zur Lösung

\int_{1}^{2} ln (1 + x) d x

Wende U-Substitution an

= \int_{2}^{3} ln (u) d u

Wende die partielle Integration an

= [u ln (u) - \int 1 d u]_{2}^{3}

\int 1 d u = u

= [u ln (u) - u]_{2}^{3}

Berechne die Grenzen:

3 ln (3) - 1 - 2 ln (2)

= 3 ln (3) - 1 - 2 ln (2)

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

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

\int_{1}^{x} sin (t^{2}) d t

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

\int_{0}^{2} (4 x - e^{x}) d x