What is the integral of 8/(7+8x) ?

The integral of 8/(7+8x) is ln|7+8x|+C

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integral of 8/(7+8x)

\int \frac{8}{7 + 8 x} d x

ln ∣ 7 + 8 x ∣ + C

Solution steps

\int \frac{8}{7 + 8 x} d x

Take the constant out:

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

= 8 \cdot \int \frac{1}{7 + 8 x} d x

Apply u-substitution

: \int \frac{1}{8 u} d u

= 8 \cdot \int \frac{1}{8 u} d u

Take the constant out:

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

= 8 \cdot \frac{1}{8} \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= 8 \cdot \frac{1}{8} ln ∣ u ∣

Substitute back

u = 7 + 8 x

= 8 \cdot \frac{1}{8} ln ∣ 7 + 8 x ∣

Simplify

8 \cdot \frac{1}{8} ln ∣ 7 + 8 x ∣ : ln ∣ 7 + 8 x ∣

= ln ∣ 7 + 8 x ∣

Add a constant to the solution

= ln ∣ 7 + 8 x ∣ + C

f (x) = - x^{2} + 4, y + 2 x - 4 = 0

7 - 3 x

\int_{\frac{1}{2}}^{2} \frac{1}{x ^{2}} d x

e^{x}, e^{4 x}, [0, 1]

x^{3} + 2 x