What is the integral of 1/((5t+2)) ?

The integral of 1/((5t+2)) is 1/5 ln|5t+2|+C

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integral of 1/((5t+2))

integral

\frac{1}{( 5 t + 2 )}

\frac{1}{5} ln ∣ 5 t + 2 ∣ + C

Solution steps

\int \frac{1}{5 t + 2} d t

Apply u-substitution

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

= \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

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

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{1}{5} ln ∣ u ∣

Substitute back

u = 5 t + 2

= \frac{1}{5} ln ∣ 5 t + 2 ∣

Add a constant to the solution

= \frac{1}{5} ln ∣ 5 t + 2 ∣ + C

1 + e^{v}

y^{2} ((1 - y^{2})^{\frac{1}{2}})

x^{4} + 2 x + 3

\frac{( e ^{x} )}{x ^{- 1}}

2 y lo g_{10} (y) + 1

What is the integral of 1/((5t+2)) ?
The integral of 1/((5t+2)) is 1/5 ln|5t+2|+C