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人気のある微分積分 >

integral from cos(x) to e^x of x^2

解

\int_{c o s (x)}^{e^{x}} x^{2} d x

解

\frac{e ^{3 x} - cos ^{3} ( x )}{3}

解答ステップ

\int_{c o s (x)}^{e^{x}} x^{2} d x

べき乗則を適用する

= [\frac{x ^{3}}{3}]_{c o s (x)}^{e^{x}}

限度を計算する:

\frac{1}{3} e^{3 x} - \frac{cos ^{3} ( x )}{3}

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

簡素化

= \frac{e ^{3 x} - cos ^{3} ( x )}{3}

人気の例

integral from 1 to 3 of 7x

\int_{1}^{3} 7 x d x

integral from 1 to 2 of (v^3+5v^6)/(v^2)

\int_{1}^{2} \frac{v ^{3} + 5 v ^{6}}{v ^{2}} d v

integral from 2 to 5 of ln(x^2-2)

\int_{2}^{5} ln (x^{2} - 2) d x

integral from 0 to ln(x) of (xe^{-y})

\int_{0}^{l n (x)} (x e^{- y}) d y

integral from-2 to 1 of 1/(x^3)

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