What is the integral of 1/(7+5x) ?

The integral of 1/(7+5x) is 1/5 ln|7+5x|+C

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integral of 1/(7+5x)

\int \frac{1}{7 + 5 x} d x

\frac{1}{5} ln ∣ 7 + 5 x ∣ + C

Solution steps

\int \frac{1}{7 + 5 x} d x

Apply u-substitution

: \int \frac{1}{5 u} d u

= \int \frac{1}{5 u} d u

Take the constant out:

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

= \frac{1}{5} \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{1}{5} ln ∣ u ∣

Substitute back

u = 7 + 5 x

= \frac{1}{5} ln ∣ 7 + 5 x ∣

Add a constant to the solution

= \frac{1}{5} ln ∣ 7 + 5 x ∣ + C

f (x) = \frac{x - 1}{x + 1}, at x = 0

\frac{d}{d x} ((x + c)^{2})

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

y^{^{'}} = \frac{5 x ^{5} e ^{\frac{y}{x}} + x ^{3} y ^{2}}{x ^{4} y}

\int (\frac{x + 5}{x ^{2} + 5 x + 6}) d x