What is the integral of 4/(5t+2) ?

The integral of 4/(5t+2) is 4/5 ln|5t+2|+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 4/(5t+2)

\int \frac{4}{5 t + 2} d t

\frac{4}{5} ln ∣ 5 t + 2 ∣ + C

Solution steps

\int \frac{4}{5 t + 2} d t

Take the constant out:

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

= 4 \cdot \int \frac{1}{5 t + 2} d t

Apply u-substitution

: \int \frac{1}{5 u} d u

= 4 \cdot \int \frac{1}{5 u} d u

Take the constant out:

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

= 4 \cdot \frac{1}{5} \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= 4 \cdot \frac{1}{5} ln ∣ u ∣

Substitute back

u = 5 t + 2

= 4 \cdot \frac{1}{5} ln ∣ 5 t + 2 ∣

Simplify

4 \cdot \frac{1}{5} ln ∣ 5 t + 2 ∣ : \frac{4}{5} ln ∣ 5 t + 2 ∣

= \frac{4}{5} ln ∣ 5 t + 2 ∣

Add a constant to the solution

= \frac{4}{5} ln ∣ 5 t + 2 ∣ + C

\int cos^{2} (t) sin^{5} (d) t

\int \frac{1 0 ^{x} + 1}{1 0 ^{x} - 1} d x

\int arctan (x^{\frac{1}{3}}) d x

\int \frac{y}{y + 3} d y

\int e^{2 x} (1 - e^{2 x})^{\frac{3}{2}} d x