integral from 1 to 4 of x-3ln(x)-2/x

Lösung

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

- 28 ln (2) + \frac{33}{2}

Dezimale

- 2.90812 \dots

Schritte zur Lösung

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

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

\int_{1}^{4} 3 ln (x) d x = 3 (8 ln (2) - 3)

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

= \frac{15}{2} - 3 (8 ln (2) - 3) - 4 ln (2)

Vereinfache

\frac{15}{2} - 3 (8 ln (2) - 3) - 4 ln (2) : - 28 ln (2) + \frac{33}{2}

= - 28 ln (2) + \frac{33}{2}

\int_{4}^{10} \frac{x}{4} - \frac{4}{x} d x

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

\int_{0}^{2} \frac{32}{x ^{2} + 4} d x

\int_{1}^{3} \frac{y}{( y + 1 ) ( y ^{2} + 2 )} d y

\int_{1}^{7} t^{2} - 2 t - 15 d t