integral from 0 to 1 of xe^{8x}

Lösung

\int_{0}^{1} x e^{8 x} d x

\frac{7 e ^{8} + 1}{64}

Dezimale

326.05790 \dots

Schritte zur Lösung

\int_{0}^{1} x e^{8 x} d x

Wende U-Substitution an

= \int_{0}^{8} \frac{e ^{u} u}{64} d u

Entferne die Konstante:

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

= \frac{1}{64} \cdot \int_{0}^{8} e^{u} u d u

Wende die partielle Integration an

= \frac{1}{64} [e^{u} u - \int e^{u} d u]_{0}^{8}

\int e^{u} d u = e^{u}

= \frac{1}{64} [e^{u} u - e^{u}]_{0}^{8}

Berechne die Grenzen:

7 e^{8} + 1

= \frac{1}{64} (7 e^{8} + 1)

Vereinfache

= \frac{7 e ^{8} + 1}{64}

\int \frac{1}{x 4 - 9 ln ^{2} ( x )} d x

t an g e n t f (x) = sin (2 x), at x = - \frac{π}{3}

d er i v a t i v e \frac{( x ^{2} - 1 ) ^{3}}{x ^{2} + 2}

\int (- sec^{2} (x)) d x

\int e^{4 x + 1} d x