What is the integral of (60x)/(5x^2+e) ?

The integral of (60x)/(5x^2+e) is 6ln|5x^2+e|+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (60x)/(5x^2+e)

\int \frac{60 x}{5 x ^{2} + e} d x

6 ln 5 x^{2} + e + C

Solution steps

\int \frac{60 x}{5 x ^{2} + e} d x

Take the constant out:

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

= 60 \cdot \int \frac{x}{5 x ^{2} + e} d x

Apply u-substitution

: \int \frac{1}{10 u} d u

= 60 \cdot \int \frac{1}{10 u} d u

Take the constant out:

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

= 60 \cdot \frac{1}{10} \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= 60 \cdot \frac{1}{10} ln ∣ u ∣

Substitute back

u = 5 x^{2} + e

= 60 \cdot \frac{1}{10} ln 5 x^{2} + e

Simplify

60 \cdot \frac{1}{10} ln 5 x^{2} + e : 6 ln 5 x^{2} + e

= 6 ln 5 x^{2} + e

Add a constant to the solution

= 6 ln 5 x^{2} + e + C

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

\int \frac{y ^{2} + 36 y + 324}{( y ^{2} + 324 ) ^{2}} d y

\int \frac{1}{csc ( 2 x ) - cot ( 2 x )} d x

\int_{4}^{8} \frac{1}{x} d x

x \to 3 lim (\frac{x - 3}{3 - x})

What is the integral of (60x)/(5x^2+e) ?
The integral of (60x)/(5x^2+e) is 6ln|5x^2+e|+C