What is the integral of (3cos(ln|x|))/x ?

The integral of (3cos(ln|x|))/x is 3sin(ln|x|)+C

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integral of (3cos(ln|x|))/x

\int \frac{3 cos ( ln ∣ x ∣ )}{x} d x

3 sin (ln ∣ x ∣) + C

Solution steps

\int \frac{3 cos ( ln ∣ x ∣ )}{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{cos ( ln ∣ x ∣ )}{x} d x

Apply u-substitution

: \int cos (u) d u

= 3 \cdot \int cos (u) d u

Use the common integral:

\int cos (u) d u = sin (u)

= 3 sin (u)

Substitute back

u = ln ∣ x ∣

= 3 sin (ln ∣ x ∣)

Add a constant to the solution

= 3 sin (ln ∣ x ∣) + C

x \to 0 lim (x tan (x))

\frac{x ^{6} + 3 x ^{2} + 50}{x ^{2} + 1}

f (x) = \frac{2 x}{( x ^{3} - 9 ) ^{2}}

\frac{d}{d x} (cot (6 x))

f (x) = 7 x + 11, (2, 5)

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