What is the integral of (2cos(ln(x)))/x ?

The integral of (2cos(ln(x)))/x is 2sin(ln(x))+C

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integral of (2cos(ln(x)))/x

\int \frac{2 cos ( ln ( x ) )}{x} d x

2 sin (ln (x)) + C

Solution steps

\int \frac{2 cos ( ln ( x ) )}{x} d x

Take the constant out:

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

= 2 \cdot \int \frac{cos ( ln ( x ) )}{x} d x

Apply u-substitution

: \int cos (u) d u

= 2 \cdot \int cos (u) d u

Use the common integral:

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

= 2 sin (u)

Substitute back

u = ln (x)

= 2 sin (ln (x))

Add a constant to the solution

= 2 sin (ln (x)) + C

\frac{\partial}{\partial y} (e^{x^{y}})

\frac{\partial}{\partial x} ((a + x)^{2} + y^{2})

\int \frac{5}{cos ^{2} ( x )} d x

\frac{d ^{2} y}{d x ^{2}} + 14 \frac{d y}{d x} + 98 y = 0

(3 x y^{2} + 1 y) d x + (3 x^{2} y + 1 x) d y = 0

What is the integral of (2cos(ln(x)))/x ?
The integral of (2cos(ln(x)))/x is 2sin(ln(x))+C