What is the integral of 7/(6+7x) ?

The integral of 7/(6+7x) is ln|6+7x|+C

Popular >

integral of 7/(6+7x)

\int \frac{7}{6 + 7 x} d x

ln ∣ 6 + 7 x ∣ + C

Solution steps

\int \frac{7}{6 + 7 x} d x

Take the constant out:

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

= 7 \cdot \int \frac{1}{6 + 7 x} d x

Apply u-substitution

: \int \frac{1}{7 u} d u

= 7 \cdot \int \frac{1}{7 u} d u

Take the constant out:

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

= 7 \cdot \frac{1}{7} \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= 7 \cdot \frac{1}{7} ln ∣ u ∣

Substitute back

u = 6 + 7 x

= 7 \cdot \frac{1}{7} ln ∣ 6 + 7 x ∣

Simplify

7 \cdot \frac{1}{7} ln ∣ 6 + 7 x ∣ : ln ∣ 6 + 7 x ∣

= ln ∣ 6 + 7 x ∣

Add a constant to the solution

= ln ∣ 6 + 7 x ∣ + C

x \to 9 lim (\frac{x + 9}{x - 9})

\frac{d}{d x} (sin (ln (1 - 3 x)))

\frac{d}{d t} (\frac{d x}{d t}) + x = sin (2 t)

\int_{0}^{\infty} 8 sin^{2} (a) d a

y^{^{''}} - 10 y^{^{'}} + 25 y = e^{5 x}