integral from 1 to 3 of (ln(3x)-ln(x))

Lösung

\int_{1}^{3} (ln (3 x) - ln (x)) d x

2 ln (3)

Dezimale

2.19722 \dots

Schritte zur Lösung

\int_{1}^{3} ln (3 x) - ln (x) d x

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{1}^{3} ln (3 x) d x - \int_{1}^{3} ln (x) d x

\int_{1}^{3} ln (3 x) d x = 5 ln (3) - 2

\int_{1}^{3} ln (x) d x = 3 ln (3) - 2

= 5 ln (3) - 2 - (3 ln (3) - 2)

Vereinfache

5 ln (3) - 2 - (3 ln (3) - 2) : 2 ln (3)

= 2 ln (3)

\int_{1}^{3} (1 - 3 x^{2}) d x

\int_{0}^{2} π (4 - y^{2})^{2} d y

\int_{2}^{3} 95 + 1200 x^{2} - 20 x d x

\int_{0}^{1} 4 x e^{x} d x

\int_{1}^{4} e^{x} - \frac{1}{x} d x