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人気のある微分積分 >

integral from pi to ln(x) of cos(e^t)

解

\int_{π}^{l n (x)} cos (e^{t}) d t

解

Ci (x) - Ci (e^{π})

解答ステップ

\int_{π}^{l n (x)} cos (e^{t}) d t

u置換積分法を適用する

= \int_{e^{π}}^{x} \frac{cos ( u )}{u} d u

非初等積分を使用する:

\int \frac{cos ( x )}{x} d x = Ci (x)

= [Ci (u)]_{e^{π}}^{x}

限度を計算する:

Ci (x) - Ci (e^{π})

= Ci (x) - Ci (e^{π})

人気の例

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

\int_{1}^{2} \frac{2 x}{( x ^{2} + 3 ) ^{3}} d x

integral from-2 to 2 of x^2(x+2)

\int_{- 2}^{2} x^{2} (x + 2) d x

integral from 1 to 6 of 1/(sqrt(x^2+2x))

\int_{1}^{6} \frac{1}{x ^{2} + 2 x} d x

integral from 0 to 1 of 1/(sqrt(4-x))

\int_{0}^{1} \frac{1}{4 - x} d x

integral from 6 to 11 of 4x-10xe^{-0.2x}

\int_{6}^{11} 4 x - 10 x e^{- 0.2 x} d x