What is the integral of (cos(ln(x+1)))/(x+1) ?

The integral of (cos(ln(x+1)))/(x+1) is sin(ln(x+1))+C

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integral of (cos(ln(x+1)))/(x+1)

\int \frac{cos ( ln ( x + 1 ) )}{x + 1} d x

sin (ln (x + 1)) + C

Solution steps

\int \frac{cos ( ln ( x + 1 ) )}{x + 1} d x

Apply u-substitution

= \int \frac{cos ( ln ( u ) )}{u} d u

Apply u-substitution

= \int cos (v) d v

Use the common integral:

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

= sin (v)

Substitute back

= sin (ln (x + 1))

Add a constant to the solution

= sin (ln (x + 1)) + C

What is the integral of (cos(ln(x+1)))/(x+1) ?
The integral of (cos(ln(x+1)))/(x+1) is sin(ln(x+1))+C