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Beliebt Rechnen >

integral from 0 to 1 of (2e^x-5/(e^x))^2

Lösung

\int_{0}^{1} (2 e^{x} - \frac{5}{e ^{x}})^{2} d x

Lösung

2 e^{2} + \frac{25 ( e ^{2} - 1 )}{2 e ^{2}} - 22

+1

Dezimale

3.58642 \dots

Schritte zur Lösung

\int_{0}^{1} (2 e^{x} - \frac{5}{e ^{x}})^{2} d x

Vereinfache

(2 e^{x} - \frac{5}{e ^{x}})^{2} : 4 e^{2 x} - 20 + \frac{25}{e ^{2 x}}

= \int_{0}^{1} 4 e^{2 x} - 20 + \frac{25}{e ^{2 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} 4 e^{2 x} d x - \int_{0}^{1} 20 d x + \int_{0}^{1} \frac{25}{e ^{2 x}} d x

\int_{0}^{1} 4 e^{2 x} d x = 2 (e^{2} - 1)

\int_{0}^{1} 20 d x = 20

\int_{0}^{1} \frac{25}{e ^{2 x}} d x = \frac{25 ( e ^{2} - 1 )}{2 e ^{2}}

= 2 (e^{2} - 1) - 20 + \frac{25 ( e ^{2} - 1 )}{2 e ^{2}}

Vereinfache

2 (e^{2} - 1) - 20 + \frac{25 ( e ^{2} - 1 )}{2 e ^{2}} : 2 e^{2} + \frac{25 ( e ^{2} - 1 )}{2 e ^{2}} - 22

= 2 e^{2} + \frac{25 ( e ^{2} - 1 )}{2 e ^{2}} - 22

Graph

Beliebte Beispiele

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\int_{10}^{x} 9 t^{2} d t

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\int_{0}^{5} x (5) d x

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\int_{0}^{5} (x 25 - x^{2}) d x

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\int_{- 4}^{2} ∣ x ∣ d x