integral from 1 to e^4 of (5-x)e^x

Lösung

\int_{1}^{e^{4}} (5 - x) e^{x} d x

- e^{e^{4} + 4} + 6 e^{e^{4}} - 5 e

Dezimale

- 2.50204 E 25

Schritte zur Lösung

\int_{1}^{e^{4}} (5 - x) e^{x} d x

Wende die partielle Integration an

= [e^{x} (5 - x) - \int - e^{x} d x]_{1}^{e^{4}}

\int - e^{x} d x = - e^{x}

= [e^{x} (5 - x) - (- e^{x})]_{1}^{e^{4}}

Vereinfache

[e^{x} (5 - x) - (- e^{x})]_{1}^{e^{4}} : [- e^{x} x + 6 e^{x}]_{1}^{e^{4}}

= [- e^{x} x + 6 e^{x}]_{1}^{e^{4}}

Berechne die Grenzen:

- e^{e^{4} + 4} + 6 e^{e^{4}} - 5 e

= - e^{e^{4} + 4} + 6 e^{e^{4}} - 5 e

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

\int_{0}^{0.37} ln (1 + x^{2}) d x

\int_{0}^{2 π} \frac{1 + cos ( 2 x )}{2} d x

\int_{- \infty}^{- 3} \frac{x}{4 - x ^{2}} d x

\int_{0}^{4} 3 x^{3} d x