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人気のある微分積分 >

integral of 1+e^{x^2}

解

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

解

x + \frac{π}{2} erfi (x) + C

解答ステップ

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

総和規則を適用する:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int 1 d x + \int e^{x^{2}} d x

\int 1 d x = x

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

= x + \frac{π}{2} erfi (x)

定数を解答に追加する

= x + \frac{π}{2} erfi (x) + C

人気の例

(\partial)/(\partial y)(e^{x^2+y^2}*2y)

\frac{\partial}{\partial y} (e^{x^{2} + y^{2}} \cdot 2 y)

integral of (x^{1/3}-3)/(x^{2/3)}

\int \frac{x ^{\frac{1}{3}} - 3}{x ^{\frac{2}{3}}} d x

integral from 0 to 2 of sqrt(1+4x^2)

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

q^'+q/(20+t)=1,q(0)=5

q^{^{'}} + \frac{q}{20 + t} = 1, q (0) = 5

derivative x^8(x-3)^7

d er i v a t i v e x^{8} (x - 3)^{7}