integral from 1 to 4 of xln(2)+3/(2x)

Lösung

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

\frac{21}{2} ln (2)

Dezimale

7.27804 \dots

Schritte zur Lösung

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

\int_{1}^{4} x ln (2) d x = ln (2) \frac{15}{2}

\int_{1}^{4} \frac{3}{2 x} d x = 3 ln (2)

= ln (2) \frac{15}{2} + 3 ln (2)

Vereinfache

ln (2) \frac{15}{2} + 3 ln (2) : \frac{21}{2} ln (2)

= \frac{21}{2} ln (2)

\int_{0}^{3} π (4 x^{2})^{2} d x

\int_{0}^{1} 4 - x^{2} d x

\int_{0}^{3} x (9 - x^{2}) d x

\int_{4}^{9} \frac{2 + x}{2 x} d x

\int_{0}^{5} s 25 - s^{2} d s