What is the integral of (11)/(ax+ ?

The integral of (11)/(ax+ is (11)/a ln|ax+d|+C

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integral of (11)/(ax+

\int \frac{11}{a x + d} d x

\frac{11}{a} ln ∣ a x + d ∣ + C

Solution steps

\int \frac{11}{a x + d} d x

Take the constant out:

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

= 11 \cdot \int \frac{1}{a x + d} d x

Apply u-substitution

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

= 11 \cdot \int \frac{1}{a u} d u

Take the constant out:

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

= 11 \cdot \frac{1}{a} \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= 11 \cdot \frac{1}{a} ln ∣ u ∣

Substitute back

u = a x + d

= 11 \cdot \frac{1}{a} ln ∣ a x + d ∣

Simplify

11 \cdot \frac{1}{a} ln ∣ a x + d ∣ : \frac{11}{a} ln ∣ a x + d ∣

= \frac{11}{a} ln ∣ a x + d ∣

Add a constant to the solution

= \frac{11}{a} ln ∣ a x + d ∣ + C

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What is the integral of (11)/(ax+ ?
The integral of (11)/(ax+ is (11)/a ln|ax+d|+C