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Popular >

integral of (cos(ln(x)))/(10x)

Solution

\int \frac{cos ( ln ( x ) )}{10 x} d x

Solution

\frac{1}{10} sin (ln (x)) + C

Solution steps

\int \frac{cos ( ln ( x ) )}{10 x} d x

Take the constant out:

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

= \frac{1}{10} \cdot \int \frac{cos ( ln ( x ) )}{x} d x

Apply u-substitution

: \int cos (u) d u

= \frac{1}{10} \cdot \int cos (u) d u

Use the common integral:

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

= \frac{1}{10} sin (u)

Substitute back

u = ln (x)

= \frac{1}{10} sin (ln (x))

Add a constant to the solution

= \frac{1}{10} sin (ln (x)) + C

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Frequently Asked Questions (FAQ)

What is the integral of (cos(ln(x)))/(10x) ?
The integral of (cos(ln(x)))/(10x) is 1/10 sin(ln(x))+C