What is the integral from a to x of (f(t))/(t^2) ?

The integral from a to x of (f(t))/(t^2) is f(ln|x|-ln|a|)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from a to x of (f(t))/(t^2)

\int_{a}^{x} \frac{f ( t )}{t ^{2}} d t

f (ln ∣ x ∣ - ln ∣ a ∣)

Solution steps

\int_{a}^{x} \frac{f t}{t ^{2}} d t

Take the constant out:

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

= f \cdot \int_{a}^{x} \frac{t}{t ^{2}} d t

Cancel the common factor:

t

= f \cdot \int_{a}^{x} \frac{1}{t} d t

Use the common integral:

\int \frac{1}{t} d t = ln (∣ t ∣)

= f [ln ∣ t ∣]_{a}^{x}

Compute the boundaries:

ln ∣ x ∣ - ln ∣ a ∣

= f (ln ∣ x ∣ - ln ∣ a ∣)

\int_{0}^{3} arctan (x) d x

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

\int_{1}^{5} 2 x - 1 d x

\int_{0}^{t} e^{- 3 x} d x

\int_{1}^{7} (x^{2} - 4 x + 4) d x

What is the integral from a to x of (f(t))/(t^2) ?
The integral from a to x of (f(t))/(t^2) is f(ln|x|-ln|a|)