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人気のある微分積分 >

integral of (e^x2^{e^x}+2xe^{x^2})

解

\int (e^{x} 2^{e^{x}} + 2 x e^{x^{2}}) d x

解

\frac{2 ^{e^{x}}}{ln ( 2 )} + e^{x^{2}} + C

解答ステップ

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

u置換積分法を適用する

= \int \frac{2 ^{u} u + 2 e ^{l n^{2} (u)} ln ( u )}{u} d u

拡張

\frac{2 ^{u} u + 2 e ^{l n^{2} (u)} ln ( u )}{u} : 2^{u} + \frac{2 e ^{l n^{2} (u)} ln ( u )}{u}

= \int 2^{u} + \frac{2 e ^{l n^{2} (u)} ln ( u )}{u} d u

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 2^{u} d u + \int \frac{2 e ^{l n^{2} (u)} ln ( u )}{u} d u

\int 2^{u} d u = \frac{2 ^{u}}{ln ( 2 )}

\int \frac{2 e ^{l n^{2} (u)} ln ( u )}{u} d u = e^{l n^{2} (u)}

= \frac{2 ^{u}}{ln ( 2 )} + e^{l n^{2} (u)}

代用を戻す

u = e^{x}

= \frac{2 ^{e^{x}}}{ln ( 2 )} + e^{l n^{2} (e^{x})}

簡素化

ln (e^{x}) : x

= \frac{2 ^{e^{x}}}{ln ( 2 )} + e^{x^{2}}

定数を解答に追加する

= \frac{2 ^{e^{x}}}{ln ( 2 )} + e^{x^{2}} + C

グラフ

人気の例

integral of 6sqrt(x)-\sqrt[6]{x}

\int 6 x - 6 x d x

integral of 2sqrt(4-x)

\int 2 4 - x d x

integral of u/(sqrt(4-9u^2))

\int \frac{u}{4 - 9 u ^{2}} d u

integral of sin^3(x)+sin^2(x)

\int sin^{3} (x) + sin^{2} (x) d x

integral of ((-1)/x)

\int (\frac{- 1}{x}) d x