Check the solution to "Evaluate the following integrals. Include absolute values only..."

Josalynn

Answered question

2021-10-15

Evaluate the following integrals. Include absolute values only when needed.

\int \frac{\sin (\ln x)}{4 x} d x

Talisha

Skilled2021-10-16Added 93 answers

It is given that,

\int \frac{\sin (\ln (x))}{4 x} d x

We have to evaluate it.
We have,

\int \frac{\sin (\ln (x))}{4 x} d x

Let

u = \ln (x)

differentiate equation w.r.t x we get

d u = \frac{1}{x} d x, \Rightarrow d x = x d u

Then equation becomes

\Rightarrow \int \frac{\sin (\ln (x))}{4 x} d x = \frac{1}{4} \int \sin (u) d u

\Rightarrow \int \frac{\sin (\ln (x))}{4 x} d x = \frac{1}{4} (- \cos (u)) + C

, where C is arbitrary constant
Putting the value of

u = \ln (x)

in above equation, we get

\Rightarrow \int \frac{\sin (\ln (x))}{4 x} d x = \frac{1}{4} (- \cos (u)) + C

Hence,

\int \frac{\sin (\ln (x))}{4 x} d x = \frac{\cos (\ln (x))}{4} + C

Do you have a similar question?

Recalculate according to your conditions!

Didn't find what you were looking for?