What is the integral of (100+2x)^{-1} ?

The integral of (100+2x)^{-1} is 1/2 ln|100+2x|+C

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integral of (100+2x)^{-1}

integral

(100 + 2 x)^{- 1}

\frac{1}{2} ln ∣ 100 + 2 x ∣ + C

Solution steps

\int (100 + 2 x)^{- 1} d x

Apply exponent rule:

a^{- 1} = \frac{1}{a}

= \int \frac{1}{100 + 2 x} d x

Apply u-substitution

= \int \frac{1}{2 u} d u

Take the constant out:

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

= \frac{1}{2} \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{1}{2} ln ∣ u ∣

Substitute back

u = 100 + 2 x

= \frac{1}{2} ln ∣ 100 + 2 x ∣

Add a constant to the solution

= \frac{1}{2} ln ∣ 100 + 2 x ∣ + C

What is the integral of (100+2x)^{-1} ?
The integral of (100+2x)^{-1} is 1/2 ln|100+2x|+C