integral from x to 3 of cos(t^3)

Lösung

\int_{x}^{3} cos (t^{3}) d t

- \frac{3 ( 3 i 3 ^{3} Γ ( \frac{1}{3} , - i 3 ^{3} ) + 3 - i 3 ^{3} Γ ( \frac{1}{3} , i 3 ^{3} ) )}{6 3 3 ^{6}} - - \frac{x ( 3 i x ^{3} Γ ( \frac{1}{3} , - i x ^{3} ) + 3 - i x ^{3} Γ ( \frac{1}{3} , i x ^{3} ) )}{6 3 x ^{6}}

Schritte zur Lösung

\int_{x}^{3} cos (t^{3}) d t

Das ist ein nicht elementares Integral :

\int cos (x^{3}) d x = - \frac{x ( 3 i x ^{3} Γ ( \frac{1}{3} , - i x ^{3} ) + 3 - i x ^{3} Γ ( \frac{1}{3} , i x ^{3} ) )}{6 3 x ^{6}}

= - \frac{t ( 3 i t ^{3} Γ ( \frac{1}{3} , - i t ^{3} ) + 3 - i t ^{3} Γ ( \frac{1}{3} , i t ^{3} ) )}{6 3 t ^{6}}_{x}^{3}

Berechne die Grenzen:

- \frac{3 ( 3 i 3 ^{3} Γ ( \frac{1}{3} , - i 3 ^{3} ) + 3 - i 3 ^{3} Γ ( \frac{1}{3} , i 3 ^{3} ) )}{6 3 3 ^{6}} - - \frac{x ( 3 i x ^{3} Γ ( \frac{1}{3} , - i x ^{3} ) + 3 - i x ^{3} Γ ( \frac{1}{3} , i x ^{3} ) )}{6 3 x ^{6}}

= - \frac{3 ( 3 i 3 ^{3} Γ ( \frac{1}{3} , - i 3 ^{3} ) + 3 - i 3 ^{3} Γ ( \frac{1}{3} , i 3 ^{3} ) )}{6 3 3 ^{6}} - - \frac{x ( 3 i x ^{3} Γ ( \frac{1}{3} , - i x ^{3} ) + 3 - i x ^{3} Γ ( \frac{1}{3} , i x ^{3} ) )}{6 3 x ^{6}}

\int_{0}^{5} π x d x

\int_{0}^{2} (x^{2} e^{x^{3}}) d x

\int_{0}^{2} \frac{4 x}{2 + x ^{2}} d x

\int_{0}^{2} 4 x + 1 d x

\int_{1}^{3} - x^{3} + 4 x^{2} - 3 x d x