What is the integral of (cos(ln(v)))/v ?

The integral of (cos(ln(v)))/v is sin(ln(v))+C

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integral of (cos(ln(v)))/v

\int \frac{cos ( ln ( v ) )}{v} d v

sin (ln (v)) + C

Solution steps

\int \frac{cos ( ln ( v ) )}{v} d v

Apply u-substitution

: \int cos (u) d u

= \int cos (u) d u

Use the common integral:

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

= sin (u)

Substitute back

u = ln (v)

= sin (ln (v))

Add a constant to the solution

= sin (ln (v)) + C

\int 3 ln (2 x) d x

\int \frac{3 x}{3} d x

\int \frac{x}{2 x + 1} d x

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

\int sin (x) - sec (x) tan (x) d x

What is the integral of (cos(ln(v)))/v ?
The integral of (cos(ln(v)))/v is sin(ln(v))+C