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 3x of (t^2+t)

解

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

解

9 x^{3} - \frac{1}{3} + \frac{9 x ^{2} - 1}{2}

解答ステップ

\int_{1}^{3 x} t^{2} + t d t

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}^{3 x} t^{2} d t + \int_{1}^{3 x} t d t

\int_{1}^{3 x} t^{2} d t = 9 x^{3} - \frac{1}{3}

\int_{1}^{3 x} t d t = \frac{9 x ^{2} - 1}{2}

= 9 x^{3} - \frac{1}{3} + \frac{9 x ^{2} - 1}{2}

人気の例

tangent f(x)=2-2x^2,-16,\at x=3

t an g e n t f (x) = 2 - 2 x^{2}, - 16, at x = 3

limit as x approaches-4 of 10x^2+34x-24

x \to - 4 lim (10 x^{2} + 34 x - 24)

sum from n=1 to infinity of 2-5(0.9)^n

n = 1 \sum \infty 2 - 5 (0.9)^{n}

sum from n=0 to infinity of 1/n-1/(n+1)

n = 0 \sum \infty \frac{1}{n} - \frac{1}{n + 1}

limit as x approaches-5-of (x+2)/(x+5)

x \to - 5 - lim (\frac{x + 2}{x + 5})