What is the integral of (cot(sqrt(x)))/(sqrt(x)) ?

The integral of (cot(sqrt(x)))/(sqrt(x)) is 2ln|sin(sqrt(x))|+C

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integral of (cot(sqrt(x)))/(sqrt(x))

\int \frac{cot ( x )}{x} d x

2 ln sin (x) + C

Solution steps

\int \frac{cot ( x )}{x} d x

Apply u-substitution

: \int 2 cot (u) d u

= \int 2 cot (u) d u

Take the constant out:

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

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

Rewrite using trig identities

= 2 \cdot \int \frac{cos ( u )}{sin ( u )} d u

Apply u-substitution

: \int \frac{1}{v} d v

= 2 \cdot \int \frac{1}{v} d v

Use the common integral:

\int \frac{1}{v} d v = ln (∣ v ∣)

= 2 ln ∣ v ∣

Substitute back

= 2 ln sin (x)

Add a constant to the solution

= 2 ln sin (x) + C

\frac{\partial}{\partial x} (ln (x + 4 y + 7 z))

\frac{d}{d x} ((x - 1)^{2} + 1)

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

\int [1 + \frac{1}{( x + 1 ) ^{2}}] d x

x \to 2 lim (4 - x)

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