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 1 to 2 of (2x^2+1)/x

解

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

解

3 + ln (2)

+1

十進法表記

3.69314 \dots

解答ステップ

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

拡張

\frac{2 x ^{2} + 1}{x} : 2 x + \frac{1}{x}

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

\int_{1}^{2} 2 x d x = 3

\int_{1}^{2} \frac{1}{x} d x = ln (2)

= 3 + ln (2)

グラフ

人気の例

integral from 1 to 7 of (x^2-8x+16)^2

\int_{1}^{7} (x^{2} - 8 x + 16)^{2} d x

integral from 0 to 3 of 2^{3x}

\int_{0}^{3} 2^{3 x} d x

integral from 0 to 2pi of-2sin^2(t)

\int_{0}^{2 π} - 2 sin^{2} (t) d t

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

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

integral from 0 to 2 of 1/(e^{x/2)+e^x}

\int_{0}^{2} \frac{1}{e ^{\frac{x}{2}} + e ^{x}} d x