integral of e^{x^3+1}

解答

\int e^{x^{3} + 1} d x

e (- \frac{x Γ ( \frac{1}{3} , - x ^{3} )}{3 3 - x ^{3}}) + C

求解步骤

\int e^{x^{3} + 1} d x

e^{x^{3} + 1} = e^{1} e^{x^{3}}

= \int e^{1} e^{x^{3}} d x

提出常数:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= e^{1} \cdot \int e^{x^{3}} d x

化简

= e \cdot \int e^{x^{3}} d x

这是非初等函数积分:

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

= e (- \frac{x Γ ( \frac{1}{3} , - x ^{3} )}{3 3 - x ^{3}})

解答补常数

= e (- \frac{x Γ ( \frac{1}{3} , - x ^{3} )}{3 3 - x ^{3}}) + C

(1 + x^{2}) y^{^{'}} - 2 x y = 0

x \to 10 lim (\frac{x ^{3}}{3})

\frac{d}{d z} (e^{2 z})

\int \frac{cos ( x )}{sin ( x )} d x

\frac{\partial}{\partial x} ((\frac{3 x ^{2}}{2 x + 4})^{3})