integral from 0 to 1 of ((e^x+3))/(e^x)

Lösung

\int_{0}^{1} \frac{( e ^{x} + 3 )}{e ^{x}} d x

- \frac{3}{e} + 4

Dezimale

2.89636 \dots

Schritte zur Lösung

\int_{0}^{1} \frac{e ^{x} + 3}{e ^{x}} d x

Multipliziere aus

\frac{e ^{x} + 3}{e ^{x}} : 1 + \frac{3}{e ^{x}}

= \int_{0}^{1} 1 + \frac{3}{e ^{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_{0}^{1} 1 d x + \int_{0}^{1} \frac{3}{e ^{x}} d x

\int_{0}^{1} 1 d x = 1

\int_{0}^{1} \frac{3}{e ^{x}} d x = 3 (- \frac{1}{e} + 1)

= 1 + 3 (- \frac{1}{e} + 1)

Vereinfache

1 + 3 (- \frac{1}{e} + 1) : - \frac{3}{e} + 4

= - \frac{3}{e} + 4

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