integral of 1/(e^{x^2)}

解答

\int \frac{1}{e ^{x^{2}}} d x

\frac{π}{2} erf (x) + C

求解步骤

\int \frac{1}{e ^{x^{2}}} d x

使用指数法则:

\frac{1}{a ^{b}} = a^{- b}

\frac{1}{e ^{x^{2}}} = e^{- x^{2}}

= \int e^{- x^{2}} d x

这是非初等函数积分:

\int e^{- x^{2}} d x = \frac{π}{2} erf (x)

= \frac{π}{2} erf (x)

解答补常数

= \frac{π}{2} erf (x) + C

\int \frac{1}{t ^{2} - 4 t + 40} d t

\int \frac{20 - 20 x}{1 - x} d x

t an g e n t f (x) = 2 x^{2} - 7 x + 5

\int \frac{x ^{3} + 2 x ^{2} - 18 x + 2}{x ^{2} + x - 12} d x

(x^{2} + 1) \frac{d y}{d x} + 3 x (y - 1) = 0, y (0) = 7