ja

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

人気のある微分積分 >

integral from 0 to x of arcsin(t)

解

\int_{0}^{x} arcsin (t) d t

解

x arcsin (x) + 1 - x^{2} - 1

解答ステップ

\int_{0}^{x} arcsin (t) d t

部分積分を適用する

= [t arcsin (t) - \int \frac{t}{1 - t ^{2}} d t]_{0}^{x}

\int \frac{t}{1 - t ^{2}} d t = - 1 - t^{2}

= [t arcsin (t) - (- 1 - t^{2})]_{0}^{x}

簡素化

= [t arcsin (t) + 1 - t^{2}]_{0}^{x}

限度を計算する:

x arcsin (x) + 1 - x^{2} - 1

= x arcsin (x) + 1 - x^{2} - 1

人気の例

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

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

integral from 1 to 2 of (x^3+4)

\int_{1}^{2} (x^{3} + 4) d x

integral from 0 to 1 of 3x^2(4x^3-5)^3

\int_{0}^{1} 3 x^{2} (4 x^{3} - 5)^{3} d x

integral from 0 to 3 of (sqrt(x^2+1))^2

\int_{0}^{3} (x^{2} + 1)^{2} d x

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

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