What is the integral of 1/(4x+3) ?

The integral of 1/(4x+3) is 1/4 ln|4x+3|+C

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integral of 1/(4x+3)

\int \frac{1}{4 x + 3} d x

\frac{1}{4} ln ∣ 4 x + 3 ∣ + C

Solution steps

\int \frac{1}{4 x + 3} d x

Apply u-substitution

: \int \frac{1}{4 u} d u

= \int \frac{1}{4 u} d u

Take the constant out:

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

= \frac{1}{4} \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{1}{4} ln ∣ u ∣

Substitute back

u = 4 x + 3

= \frac{1}{4} ln ∣ 4 x + 3 ∣

Add a constant to the solution

= \frac{1}{4} ln ∣ 4 x + 3 ∣ + C

\frac{d}{d x} (3 x^{5} + 7 x)

\frac{d}{d x} (4 x^{2} - 3 x)

\int 21 - x^{2} - 4 x d x

\frac{d}{d x} (2 x^{2} + 4 x y - x - 2 y)

y^{^{''}} - 8 y^{^{'}} + 8 y = 0