integral from 1 to 2 of 4x^2ln(x)

Lösung

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

4 (- \frac{7}{9} + \frac{8}{3} ln (2))

Dezimale

4.28245 \dots

Schritte zur Lösung

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

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

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

Wende die partielle Integration an

= 4 [\frac{1}{3} x^{3} ln (x) - \int \frac{x ^{2}}{3} d x]_{1}^{2}

\int \frac{x ^{2}}{3} d x = \frac{x ^{3}}{9}

= 4 [\frac{1}{3} x^{3} ln (x) - \frac{x ^{3}}{9}]_{1}^{2}

Berechne die Grenzen:

- \frac{7}{9} + \frac{8}{3} ln (2)

= 4 (- \frac{7}{9} + \frac{8}{3} ln (2))

t an g e n t f (x) = \frac{x}{x ^{2} + 4}, at x = 0

\int_{0}^{1} \frac{28}{x ^{2} - 49} d x

6 y^{^{''}} - 6 y^{^{'}} + 15 y = 0

\int \frac{7 x}{x ^{3} + 1} d x

d er i v a t i v e y = (x + 7) (7 x + 2)