integral from 0 to 4 of e^{(x-2)^4}

Lösung

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

- \frac{2Γ ( \frac{1}{4} , - 2 ^{4} )}{4 4 - 2 ^{4}} - - \frac{( - 2 ) Γ ( \frac{1}{4} , - ( - 2 ) ^{4} )}{4 4 - ( - 2 ) ^{4}}

Schritte zur Lösung

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

Wende U-Substitution an

= \int_{- 2}^{2} e^{u^{4}} d u

Das ist ein nicht elementares Integral :

\int e^{x^{a}} d x = - \frac{x Γ ( \frac{1}{a} , - x ^{a} )}{a a - x ^{a}}

= [- \frac{u Γ ( \frac{1}{4} , - u ^{4} )}{4 4 - u ^{4}}]_{- 2}^{2}

Berechne die Grenzen:

- \frac{2Γ ( \frac{1}{4} , - 2 ^{4} )}{4 4 - 2 ^{4}} - - \frac{( - 2 ) Γ ( \frac{1}{4} , - ( - 2 ) ^{4} )}{4 4 - ( - 2 ) ^{4}}

= - \frac{2Γ ( \frac{1}{4} , - 2 ^{4} )}{4 4 - 2 ^{4}} - - \frac{( - 2 ) Γ ( \frac{1}{4} , - ( - 2 ) ^{4} )}{4 4 - ( - 2 ) ^{4}}

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