What is the integral of 3/(50+2x) ?

The integral of 3/(50+2x) is 3/2 ln|50+2x|+C

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integral of 3/(50+2x)

\int \frac{3}{50 + 2 x} d x

\frac{3}{2} ln ∣ 50 + 2 x ∣ + C

Solution steps

\int \frac{3}{50 + 2 x} d x

Take the constant out:

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

= 3 \cdot \int \frac{1}{50 + 2 x} d x

Apply u-substitution

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

= 3 \cdot \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

= 3 \cdot \frac{1}{2} \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= 3 \cdot \frac{1}{2} ln ∣ u ∣

Substitute back

u = 50 + 2 x

= 3 \cdot \frac{1}{2} ln ∣ 50 + 2 x ∣

Simplify

3 \cdot \frac{1}{2} ln ∣ 50 + 2 x ∣ : \frac{3}{2} ln ∣ 50 + 2 x ∣

= \frac{3}{2} ln ∣ 50 + 2 x ∣

Add a constant to the solution

= \frac{3}{2} ln ∣ 50 + 2 x ∣ + C

y^{^{''}} + 6 y^{^{'}} + 8 y = e^{- 5 x}

\frac{d}{d x} (6 x^{70})

y^{^{''}} - y^{^{'}} - 2 y = - 2 t + 10 t^{2}

\int \frac{1}{5 x + 16} d x

y = 9 x^{2}, y = x^{2} + 7

What is the integral of 3/(50+2x) ?
The integral of 3/(50+2x) is 3/2 ln|50+2x|+C