integral from 1 to 3 of 13r^3ln(r)

Lösung

\int_{1}^{3} 13 r^{3} ln (r) d r

13 (- 5 + \frac{81}{4} ln (3))

Dezimale

224.20968 \dots

Schritte zur Lösung

\int_{1}^{3} 13 r^{3} ln (r) d r

Entferne die Konstante:

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

= 13 \cdot \int_{1}^{3} r^{3} ln (r) d r

Wende die partielle Integration an

= 13 [\frac{1}{4} r^{4} ln (r) - \int \frac{r ^{3}}{4} d r]_{1}^{3}

\int \frac{r ^{3}}{4} d r = \frac{r ^{4}}{16}

= 13 [\frac{1}{4} r^{4} ln (r) - \frac{r ^{4}}{16}]_{1}^{3}

Berechne die Grenzen:

- 5 + \frac{81}{4} ln (3)

= 13 (- 5 + \frac{81}{4} ln (3))

n = 0 \sum \infty 5 n

\int \frac{( 7 ( 1 - tan ^{2} ( x ) ) )}{sec ^{2} ( x )} d x

\frac{\partial}{\partial x} (ln (4 x^{2} + 7 y^{2} + 4))

\int x^{2} I n (x) d x

f (x) = 2 e^{5 x}