zs

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

受欢迎的微积分 >

integral of 3/(60-t)

解答

\int \frac{3}{60 - t} d t

解答

- 3 ln ∣ 60 - t ∣ + C

求解步骤

\int \frac{3}{60 - t} d t

提出常数:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 3 \cdot \int \frac{1}{60 - t} d t

使用换元积分法

= 3 \cdot \int - \frac{1}{u} d u

提出常数:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 3 (- \int \frac{1}{u} d u)

使用积分常见定则:

\int \frac{1}{u} d u = ln (∣ u ∣)

= 3 (- ln ∣ u ∣)

u = 60 - t

代回

= 3 (- ln ∣ 60 - t ∣)

化简

= - 3 ln ∣ 60 - t ∣

解答补常数

= - 3 ln ∣ 60 - t ∣ + C

作图

流行的例子

tangent 8/(x^2+4)

t an g e n t \frac{8}{x ^{2} + 4}

tangent f(x)=(20x)/(x^2-5)

t an g e n t f (x) = \frac{20 x}{x ^{2} - 5}

limit as x approaches-6+of 1/((x+6)^6)

x \to - 6 + lim (\frac{1}{( x + 6 ) ^{6}})

integral from 0 to 3 of-6x^2

\int_{0}^{3} - 6 x^{2} d x

tangent f(x)=2x^3-5x+4,\at x=-1

t an g e n t f (x) = 2 x^{3} - 5 x + 4, at x = - 1